Question 1

Evaluate using the change-of-base formula. Round to four decimal places.
-$\log 38$

Accepted Answer

A)  0.5283 
B)  3.7856 
C)  -1.8928 
D)  1.8928 
A)  0.5283 
B)  3.7856 
C)  -1.8928 
D)  1.8928

Question 2

$f(x)=e^{x+3}+1$

Accepted Answer

A)  Horizontal asymptote: $\mathrm{y}=1$;
Domain: $(-\infty, \infty)$, Range: $(1, \infty)$ 
B)  Horizontal asymptote: $\mathrm{y}=0$;
Domain: $(-\infty, \infty)$, Range: $(0, \infty)$ 
C)  Horizontal asymptote: $\mathrm{y}=3$;
Domain: $(-\infty, \infty)$, Range: $(3, \infty)$ 
D)  Horizontal asymptote: $\mathrm{y}=-1$;
Domain: $(-\infty, \infty)$, Range: $(-1, \infty)$ 
A)  Horizontal asymptote: $\mathrm{y}=1$;
Domain: $(-\infty, \infty)$, Range: $(1, \infty)$ 
B)  Horizontal asymptote: $\mathrm{y}=0$;
Domain: $(-\infty, \infty)$, Range: $(0, \infty)$ 
C)  Horizontal asymptote: $\mathrm{y}=3$;
Domain: $(-\infty, \infty)$, Range: $(3, \infty)$ 
D)  Horizontal asymptote: $\mathrm{y}=-1$;
Domain: $(-\infty, \infty)$, Range: $(-1, \infty)$

Question 3

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions.
-$f(x)=9 x+72, g(x)=\frac{1}{9} x-8$

Accepted Answer

A) True 
 B)False

Question 4

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function.
-$f(x)=5^{x-2}-1$

Accepted Answer

A)  Horizontal asymptote: $\mathrm{y}=-2$;
Domain: $(-\infty, \infty)$, Range: $(-2, \infty)$ 
B)  Horizontal asymptote: $\mathrm{y}=0$;
Domain: $(-\infty, \infty)$, Range: $(0, \infty)$ 
C)  Horizontal asymptote: $\mathrm{y}=1$;
Domain: $(-\infty, \infty)$, Range: $(1, \infty)$ 
D)  Horizontal asymptote: $\mathrm{y}=-1$;
Domain: $(-\infty, \infty)$, Range: $(-1, \infty)$ 
A)  Horizontal asymptote: $\mathrm{y}=-2$;
Domain: $(-\infty, \infty)$, Range: $(-2, \infty)$ 
B)  Horizontal asymptote: $\mathrm{y}=0$;
Domain: $(-\infty, \infty)$, Range: $(0, \infty)$ 
C)  Horizontal asymptote: $\mathrm{y}=1$;
Domain: $(-\infty, \infty)$, Range: $(1, \infty)$ 
D)  Horizontal asymptote: $\mathrm{y}=-1$;
Domain: $(-\infty, \infty)$, Range: $(-1, \infty)$

Question 5

The area betw een the graph of $f(x)=e^{x}$ and the $x$-axis on an interval $[a, b]$ is equal to $e^{b}-e^{a}$. Sketch the graph of $f(x)=e^{x}$, and shade the area between the graph and the $x$-axis. Find the shaded area, rounded to the nearest hundredth.
-$[0,2.5]$

Accepted Answer

A)  4.06
  
B)  13.18
  
C)  6.06
  
D)  11.18
  
A)  4.06
  
B)  13.18
  
C)  6.06
  
D)  11.18

Question 6

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions.
-$f(x)=5 x, g(x)=-5 x$

Accepted Answer

A) True 
 B)False

Question 7

For the given function $f(x)$, find $f^{-1}(x)$. State the domain of $f^{-1}(x)$.
-$f(x)=(x+16)^{2}-5(x \geq-16)$

Accepted Answer

A)  $f 1(x)=\sqrt{x+16}+5, x \geq-16$ 
B)  $f^{-1}(x)=\sqrt{x-5}+16, x \geq 5$ 
C)  $f 1(x)=5 x^{2}+16, x \geq 0$ 
D)  $f^{-1}(x)=\sqrt{x+5}-16, x \geq-5$ 
A)  $f 1(x)=\sqrt{x+16}+5, x \geq-16$ 
B)  $f^{-1}(x)=\sqrt{x-5}+16, x \geq 5$ 
C)  $f 1(x)=5 x^{2}+16, x \geq 0$ 
D)  $f^{-1}(x)=\sqrt{x+5}-16, x \geq-5$

Question 8

Evaluate. Round to the nearest thousandth, if necessary.
-$\log 0.001$

Accepted Answer

A)  3 
B)  $-\frac{1}{3}$ 
C)  $\frac{1}{3}$ 
D)  -3 
A)  3 
B)  $-\frac{1}{3}$ 
C)  $\frac{1}{3}$ 
D)  -3

Question 9

Evaluate. Round to the nearest thousandth, if necessary.
-$\ln \left(\mathrm{e}^{-9}\right)$

Accepted Answer

A)  $\frac{1}{9}$ 
B)  -9 
C)  9 
D)  $-\frac{1}{9}$ 
A)  $\frac{1}{9}$ 
B)  -9 
C)  9 
D)  $-\frac{1}{9}$

Question 10

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers.
-$\log _{3}\left(\frac{x y}{3}\right)$

Accepted Answer

A)  $\log _{3} x+\log _{3} y+\log _{3} 3$ 
B)  $\log _{3} x+\log _{3} y-\log _{3} 3$ 
C)  $(\log  _{3} x)(\log _{3} y) \div \log _{3}3$ 
D)  $\left(\log _{3} x\right)^{2}+\left(\log _{3} y\right)^{2}-\log _{3} 3$ 
A)  $\log _{3} x+\log _{3} y+\log _{3} 3$ 
B)  $\log _{3} x+\log _{3} y-\log _{3} 3$ 
C)  $(\log  _{3} x)(\log _{3} y) \div \log _{3}3$ 
D)  $\left(\log _{3} x\right)^{2}+\left(\log _{3} y\right)^{2}-\log _{3} 3$

Question 11

Graph a one-to-one function f(x) that meets the given criteria.
-$f(x)$ is a linear function, $f(-9)=5$, and $f^{-1}(-2)=-8$.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 12

A fixed point of a function $f(x)$ is a value for which $f(x)=x$. For the given function, find:
 a) Fixed point of $f(x)$
b) (f  $\circ f)(\mathbf{x})$
c) Fixed point of (f $\circ\mathbf{f})(\mathbf{x})$
-$f(x)=2 x-5$

Accepted Answer

A)  a) 5 b) $4 \mathrm{x}-15$ c) 5 
B)  a) 1 b) $4 \mathrm{x}-1$ c) 3 
C)  a) 1 b) $4 \mathrm{x}-3$ c) 1 
D)  a) -5 b) $4 \mathrm{x}+15$ c) -5 
A)  a) 5 b) $4 \mathrm{x}-15$ c) 5 
B)  a) 1 b) $4 \mathrm{x}-1$ c) 3 
C)  a) 1 b) $4 \mathrm{x}-3$ c) 1 
D)  a) -5 b) $4 \mathrm{x}+15$ c) -5

Question 13

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=x^{2}+2 x-15, g(x)=x+5$
Find $\left(\frac{f}{g}\right)(x)$.

Accepted Answer

A)  $\mathrm{x}-3$ 
B)  $x^{2}+3 x-10$ 
C)  $x+3$ 
D)  $x^{2}-3$ 
A)  $\mathrm{x}-3$ 
B)  $x^{2}+3 x-10$ 
C)  $x+3$ 
D)  $x^{2}-3$

Question 14

Solve.
-$2^{7-3 x}=\frac{1}{4}$

Accepted Answer

A)  $\{3\}$ 
B)  $\left\{\frac{1}{2}\right\}$ 
C)  $\{-3\}$ 
D)  $\{8\}$ 
A)  $\{3\}$ 
B)  $\left\{\frac{1}{2}\right\}$ 
C)  $\{-3\}$ 
D)  $\{8\}$

Question 15

Find the specified domain
-For $f(x)=x^{2}-1$ and $g(x)=2 x+3$, what is the domain of $f \circ g$ ?

Accepted Answer

A)  $[1, \infty)$ 
B)  $(-1,1)$ 
C)  $(-\infty, \infty)$ 
D)  $[0, \infty)$ 
A)  $[1, \infty)$ 
B)  $(-1,1)$ 
C)  $(-\infty, \infty)$ 
D)  $[0, \infty)$

Question 16

Solve the equation.
-$\log _{9}(\mathrm{x}-5)+\log _{9}(\mathrm{x}-5)=1$

Accepted Answer

A)  $\{-\sqrt{26}, \sqrt{26}\}$ 
B)  $\{-8,8\}$ 
C)  $\{\sqrt{26}\}$ 
D)  $\{8\}$ 
A)  $\{-\sqrt{26}, \sqrt{26}\}$ 
B)  $\{-8,8\}$ 
C)  $\{\sqrt{26}\}$ 
D)  $\{8\}$

Question 17

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of thisfunction.
-$f(x)=\left(\frac{1}{3}\right)^{x}-4$

Accepted Answer

A)  Horizontal asymptote: $\mathrm{y}=0$;
Domain: $(-\infty, \infty)$, Range: $(0, \infty)$ 
B)  Horizontal asymptote: $\mathrm{y}=4$;
Domain: $(-\infty, \infty)$, Range: $(4, \infty)$ 
C)  Horizontal asymptote: $\mathrm{y}=\frac{1}{3}$;
Domain: $(-\infty, \infty)$, Range: $\left(\frac{1}{3}, \infty\right)$ 
D)  Horizontal asymptote: $\mathrm{y}=-4$;
Domain: $(-\infty, \infty)$, Range: $(-4, \infty)$ 
A)  Horizontal asymptote: $\mathrm{y}=0$;
Domain: $(-\infty, \infty)$, Range: $(0, \infty)$ 
B)  Horizontal asymptote: $\mathrm{y}=4$;
Domain: $(-\infty, \infty)$, Range: $(4, \infty)$ 
C)  Horizontal asymptote: $\mathrm{y}=\frac{1}{3}$;
Domain: $(-\infty, \infty)$, Range: $\left(\frac{1}{3}, \infty\right)$ 
D)  Horizontal asymptote: $\mathrm{y}=-4$;
Domain: $(-\infty, \infty)$, Range: $(-4, \infty)$

Question 18

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function.
-$f(x)=\log (5 x-4)-13$

Accepted Answer

A)  Vertical asymptote: $x=\frac{4}{5}$;
Domain: $\left(\frac{4}{5}, \infty\right)$, Range: $(-\infty, \infty)$ 
B)  Vertical asymptote: $x=13$;
Domain: $(13, \infty)$, Range: $(-\infty, \infty)$ 
C)  Vertical asymptote: $x=\frac{5}{4}$;
Domain: $\left(\frac{5}{4}, \infty\right)$, Range: $(-\infty, \infty)$ 
D)  Vertical asymptote: $\mathrm{x}=\frac{4}{5}$;
Domain: $\left(\frac{4}{5}, \infty\right)$, Range: $(-\infty, \infty)$ 
A)  Vertical asymptote: $x=\frac{4}{5}$;
Domain: $\left(\frac{4}{5}, \infty\right)$, Range: $(-\infty, \infty)$ 
B)  Vertical asymptote: $x=13$;
Domain: $(13, \infty)$, Range: $(-\infty, \infty)$ 
C)  Vertical asymptote: $x=\frac{5}{4}$;
Domain: $\left(\frac{5}{4}, \infty\right)$, Range: $(-\infty, \infty)$ 
D)  Vertical asymptote: $\mathrm{x}=\frac{4}{5}$;
Domain: $\left(\frac{4}{5}, \infty\right)$, Range: $(-\infty, \infty)$

Question 19

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers.
-$\log _{\mathrm{x}} 12-\log _{\mathrm{x}} 2$

Accepted Answer

A)  $\log _{\mathrm{x}} 10$ 
B)  $\log _{\mathrm{x}} 24$ 
C)  $\log _{\mathrm{x}} 6$ 
D)  $\frac{\log _{\mathrm{x}} 12}{\log _{\mathrm{x}} 2}$ 
A)  $\log _{\mathrm{x}} 10$ 
B)  $\log _{\mathrm{x}} 24$ 
C)  $\log _{\mathrm{x}} 6$ 
D)  $\frac{\log _{\mathrm{x}} 12}{\log _{\mathrm{x}} 2}$

Question 20

Solve the problem.
-Find the hydrogen ion concentration of a solution $\left[\mathrm{H}^{+}\right]$whose $\mathrm{pH}$ is 7.3. Use the formula $\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right]$.

Accepted Answer

A)  $-8.63 \times 10^{-1}$ moles per liter 
B)  $8.63 \times 10^{-1}$ moles per liter 
C)  $5.01 \times 10^{-8}$ moles per liter 
D)  $2.00 \times 10^{7}$ moles per liter 
A)  $-8.63 \times 10^{-1}$ moles per liter 
B)  $8.63 \times 10^{-1}$ moles per liter 
C)  $5.01 \times 10^{-8}$ moles per liter 
D)  $2.00 \times 10^{7}$ moles per liter

Evaluate using the change-of-base formula. Round to four decimal places. - $\log 38$

$f(x)=e^{x+3}+1$

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=9 x+72, g(x)=\frac{1}{9} x-8$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - $f(x)=5^{x-2}-1$

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=5 x, g(x)=-5 x$

For the given function $f(x)$ , find $f^{-1}(x)$ . State the domain of $f^{-1}(x)$ . - $f(x)=(x+16)^{2}-5(x \geq-16)$

Evaluate. Round to the nearest thousandth, if necessary. - $\log 0.001$

Evaluate. Round to the nearest thousandth, if necessary. - $\ln \left(\mathrm{e}^{-9}\right)$

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers. - $\log _{3}\left(\frac{x y}{3}\right)$

Graph a one-to-one function f(x) that meets the given criteria. - $f(x)$ is a linear function, $f(-9)=5$ , and $f^{-1}(-2)=-8$ . $Graph a one-to-one function f(x) that meets the given criteria. - f(x) is a linear function, f(-9)=5 , and f^{-1}(-2)=-8 .$

A fixed point of a function $f(x)$ is a value for which $f(x)=x$ . For the given function, find: a) Fixed point of $f(x)$ b) (f $\circ f)(\mathbf{x})$ c) Fixed point of (f $\circ\mathbf{f})(\mathbf{x})$ - $f(x)=2 x-5$

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f(x)=x^{2}+2 x-15, g(x)=x+5$ Find $\left(\frac{f}{g}\right)(x)$ .

Solve. - $2^{7-3 x}=\frac{1}{4}$

Find the specified domain -For $f(x)=x^{2}-1$ and $g(x)=2 x+3$ , what is the domain of $f \circ g$ ?

Solve the equation. - $\log _{9}(\mathrm{x}-5)+\log _{9}(\mathrm{x}-5)=1$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of thisfunction. - $f(x)=\left(\frac{1}{3}\right)^{x}-4$

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function. - $f(x)=\log (5 x-4)-13$

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - $\log _{\mathrm{x}} 12-\log _{\mathrm{x}} 2$

Solve the problem. -Find the hydrogen ion concentration of a solution $\left[\mathrm{H}^{+}\right]$ whose $\mathrm{pH}$ is 7.3. Use the formula $\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right]$ .

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 9: Logarithmic and Exponential Functions

Evaluate using the change-of-base formula. Round to four decimal places. - log⁡38\log 38log38

f(x)=ex+3+1f(x)=e^{x+3}+1f(x)=ex+3+1

Determine whether the functions f(x)f(x)f(x) and g(x)g(x)g(x) are inverse functions. - f(x)=9x+72,g(x)=19x−8f(x)=9 x+72, g(x)=\frac{1}{9} x-8f(x)=9x+72,g(x)=91​x−8

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - f(x)=5x−2−1f(x)=5^{x-2}-1f(x)=5x−2−1

Determine whether the functions f(x)f(x)f(x) and g(x)g(x)g(x) are inverse functions. - f(x)=5x,g(x)=−5xf(x)=5 x, g(x)=-5 xf(x)=5x,g(x)=−5x

For the given function f(x)f(x)f(x) , find f−1(x)f^{-1}(x)f−1(x) . State the domain of f−1(x)f^{-1}(x)f−1(x) . - f(x)=(x+16)2−5(x≥−16)f(x)=(x+16)^{2}-5(x \geq-16)f(x)=(x+16)2−5(x≥−16)

Evaluate. Round to the nearest thousandth, if necessary. - log⁡0.001\log 0.001log0.001

Evaluate. Round to the nearest thousandth, if necessary. - ln⁡(e−9)\ln \left(\mathrm{e}^{-9}\right)ln(e−9)

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers. - log⁡3(xy3)\log _{3}\left(\frac{x y}{3}\right)log3​(3xy​)

Graph a one-to-one function f(x) that meets the given criteria. - f(x)f(x)f(x) is a linear function, f(−9)=5f(-9)=5f(−9)=5 , and f−1(−2)=−8f^{-1}(-2)=-8f−1(−2)=−8 .

A fixed point of a function f(x)f(x)f(x) is a value for which f(x)=xf(x)=xf(x)=x . For the given function, find: a) Fixed point of f(x)f(x)f(x) b) (f ∘f)(x)\circ f)(\mathbf{x})∘f)(x) c) Fixed point of (f ∘f)(x)\circ\mathbf{f})(\mathbf{x})∘f)(x) - f(x)=2x−5f(x)=2 x-5f(x)=2x−5

For the given functions f(x)f(x)f(x) and g(x)g(x)g(x) , find (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x) or (fg)(x)\left(\frac{f}{g}\right)(x)(gf​)(x) as indicated. - f(x)=x2+2x−15,g(x)=x+5f(x)=x^{2}+2 x-15, g(x)=x+5f(x)=x2+2x−15,g(x)=x+5 Find (fg)(x)\left(\frac{f}{g}\right)(x)(gf​)(x) .

Solve. - 27−3x=142^{7-3 x}=\frac{1}{4}27−3x=41​

Find the specified domain -For f(x)=x2−1f(x)=x^{2}-1f(x)=x2−1 and g(x)=2x+3g(x)=2 x+3g(x)=2x+3 , what is the domain of f∘gf \circ gf∘g ?

Solve the equation. - log⁡9(x−5)+log⁡9(x−5)=1\log _{9}(\mathrm{x}-5)+\log _{9}(\mathrm{x}-5)=1log9​(x−5)+log9​(x−5)=1

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of thisfunction. - f(x)=(13)x−4f(x)=\left(\frac{1}{3}\right)^{x}-4f(x)=(31​)x−4

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function. - f(x)=log⁡(5x−4)−13f(x)=\log (5 x-4)-13f(x)=log(5x−4)−13

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - log⁡x12−log⁡x2\log _{\mathrm{x}} 12-\log _{\mathrm{x}} 2logx​12−logx​2

Solve the problem. -Find the hydrogen ion concentration of a solution [H+]\left[\mathrm{H}^{+}\right][H+] whose pH\mathrm{pH}pH is 7.3. Use the formula pH=−log⁡[H+]\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right]pH=−log[H+] .

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Evaluate using the change-of-base formula. Round to four decimal places. - $\log 38$

$f(x)=e^{x+3}+1$

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=9 x+72, g(x)=\frac{1}{9} x-8$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - $f(x)=5^{x-2}-1$

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=5 x, g(x)=-5 x$

For the given function $f(x)$ , find $f^{-1}(x)$ . State the domain of $f^{-1}(x)$ . - $f(x)=(x+16)^{2}-5(x \geq-16)$

Evaluate. Round to the nearest thousandth, if necessary. - $\log 0.001$

Evaluate. Round to the nearest thousandth, if necessary. - $\ln \left(\mathrm{e}^{-9}\right)$

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers. - $\log _{3}\left(\frac{x y}{3}\right)$

Graph a one-to-one function f(x) that meets the given criteria. - $f(x)$ is a linear function, $f(-9)=5$ , and $f^{-1}(-2)=-8$ . $Graph a one-to-one function f(x) that meets the given criteria. - f(x) is a linear function, f(-9)=5 , and f^{-1}(-2)=-8 .$

A fixed point of a function $f(x)$ is a value for which $f(x)=x$ . For the given function, find: a) Fixed point of $f(x)$ b) (f $\circ f)(\mathbf{x})$ c) Fixed point of (f $\circ\mathbf{f})(\mathbf{x})$ - $f(x)=2 x-5$

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f(x)=x^{2}+2 x-15, g(x)=x+5$ Find $\left(\frac{f}{g}\right)(x)$ .

Solve. - $2^{7-3 x}=\frac{1}{4}$

Find the specified domain -For $f(x)=x^{2}-1$ and $g(x)=2 x+3$ , what is the domain of $f \circ g$ ?

Solve the equation. - $\log _{9}(\mathrm{x}-5)+\log _{9}(\mathrm{x}-5)=1$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of thisfunction. - $f(x)=\left(\frac{1}{3}\right)^{x}-4$

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function. - $f(x)=\log (5 x-4)-13$

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - $\log _{\mathrm{x}} 12-\log _{\mathrm{x}} 2$

Solve the problem. -Find the hydrogen ion concentration of a solution $\left[\mathrm{H}^{+}\right]$ whose $\mathrm{pH}$ is 7.3. Use the formula $\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right]$ .