Question 1

Solve for x . $\log _ { 81 } 27 = x$

Accepted Answer

The answer of Solve for x . \(\log _ {...

Question 2

Solve: $\log _ { 8 } x = - \frac { 1 } { 3 }$

Accepted Answer

A)  -2 
B)  2 
C)  -$\frac { 1 } { 2 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  -2 
B)  2 
C)  -$\frac { 1 } { 2 }$ 
D)  $\frac { 1 } { 2 }$

Question 3

Does $\frac { \log 7 } { \log 6 } = \log 7 - \log 6$ ?
 Answer yes or no .

Accepted Answer

The answer of Does \(\frac { \log 7 } {...

Question 4

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that h , j , k , and b are positive numbers, and $\log _ { 5 } 9$ . $\log _ { b } 7 = 0.8451$

Accepted Answer

The answer of Write the logarithm as a sum and/or...

Question 5

Write in logarithmic form: $4 ^ { 2 } = 16$

Accepted Answer

A)  $\log _ { 2 } 16 = 4$ 
B)  $\log _ { 4 } 16 = 2$ 
C)  $\log _ { 16 } 4 = 2$ 
D)  $\log _ { 4 } 2 = 16$ 
A)  $\log _ { 2 } 16 = 4$ 
B)  $\log _ { 4 } 16 = 2$ 
C)  $\log _ { 16 } 4 = 2$ 
D)  $\log _ { 4 } 2 = 16$

Question 6

Let $f ( x ) = 3 x - 4$ and $g ( x ) = x ^ { 2 } - 1$ . Find: $( f \circ g ) ( x )$

Accepted Answer

A)  $3 x ^ { 2 } - 5$ 
B)  $3 x ^ { 2 } - 7$ 
C)  $9 x ^ { 2 } - 24 x + 15$ 
D)  $3 x ^ { 2 } - 3$ 
A)  $3 x ^ { 2 } - 5$ 
B)  $3 x ^ { 2 } - 7$ 
C)  $9 x ^ { 2 } - 24 x + 15$ 
D)  $3 x ^ { 2 } - 3$

Question 7

Write the logarithm as a difference. Then simplify, if possible. Assume that x is positive number. $\log _ { 2 } \frac { x } { 8 }$

Accepted Answer

The answer of Write the logarithm as a difference. Then...

Question 8

Solve: $3 ^ { x ^ { 2 } - 3 x } = 81$

Accepted Answer

The answer of Solve: \(3 ^ { x ^ {...

Question 9

Evaluate the expression. $\log _ { 9 } 3$

Accepted Answer

The answer of Evaluate the expression. \(\log _ { 9...

Question 10

Evaluate expression without using a calculator. $\ln e ^ { 3 }$

Accepted Answer

The answer of Evaluate expression without using a calculator. \(\ln...

Question 11

Solve the equation. $\ln \left( x ^ { 2 } + 5 x \right) = \ln \left( x ^ { 2 } + 20 \right)$ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(\ln \left( x ^...

Question 12

The quantity of a prescription drug in the bloodstream of a patient t hours after it is administered can be modeled by an exponential function. (See the graph.) Determine the time it takes to eliminate half of the initial dose from the body.  __________ hr

Accepted Answer

The answer of The quantity of a prescription drug in...

Question 13

Evaluate the expression. $5 ^ { \log _ { 5 } 8 }$

Accepted Answer

The answer of Evaluate the expression. \(5 ^ { \log...

Question 14

Determine whether the function is one-to-one. $f ( x ) = | 4 x |$ Answer yes or no .

Accepted Answer

The answer of Determine whether the function is one-to-one. \(f...

Question 15

To estimate the number of hours t that a murder victim had been dead, a coroner used the formula $t = \frac { 1 } { 0.25 } \ln \frac { 98.6 - T _ { s } } { 82 - T _ { s } }$ where $T _ { s }$ is the temperature of the surroundings where the body was found. If the crime took place in an apartment where the thermostat was set at $74 ^ { \circ } \mathrm { F }$ , approximately how long ago did the murder occur?
 Please round the answer to one decimal place. about __________ hours ago

Accepted Answer

The answer of To estimate the number of hours t...

Question 16

If $\log _ { b } x ^ { 2 } = 1 + \log _ { b } 6$ , find b .

Accepted Answer

The answer of If \(\log _ { b } x...

Question 17

If $e ^ { \frac { t } { 6 } } = k ^ { t }$ find k .

Accepted Answer

The answer of If \(e ^ { \frac { t...

Question 18

Let $f ( x ) = 5 x - 4$ and $g ( x ) = x ^ { 2 } - 6$ . Find: f g

Accepted Answer

A)  $- x ^ { 2 } + 5 x + 2$ 
B)  $- x ^ { 2 } + 5 x - 10$ 
C)  $x ^ { 2 } - 5 x - 2$ 
D)  $- x ^ { 2 } + 5 x - 2$ 
A)  $- x ^ { 2 } + 5 x + 2$ 
B)  $- x ^ { 2 } + 5 x - 10$ 
C)  $x ^ { 2 } - 5 x - 2$ 
D)  $- x ^ { 2 } + 5 x - 2$

Question 19

Determine the domain and range of the logarithmic function graphed below.

Accepted Answer

The answer of Determine the domain and range of the...

Question 20

An isotope of thorium, ${ } ^ { 227 } \mathrm { Th }$ , has a half-life of 18.4 days. How long will it take for 77% of the sample to decompose?
 Please round the answer to the nearest tenth.

Accepted Answer

The answer of An isotope of thorium, \({ } ^...

Solve for x . $\log _ { 81 } 27 = x$

Solve: $\log _ { 8 } x = - \frac { 1 } { 3 }$

Does $\frac { \log 7 } { \log 6 } = \log 7 - \log 6$ ? Answer yes or no .

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that h , j , k , and b are positive numbers, and $\log _ { 5 } 9$ . $\log _ { b } 7 = 0.8451$

Write in logarithmic form: $4 ^ { 2 } = 16$

Let $f ( x ) = 3 x - 4$ and $g ( x ) = x ^ { 2 } - 1$ . Find: $( f \circ g ) ( x )$

Write the logarithm as a difference. Then simplify, if possible. Assume that x is positive number. $\log _ { 2 } \frac { x } { 8 }$

Solve: $3 ^ { x ^ { 2 } - 3 x } = 81$

Evaluate the expression. $\log _ { 9 } 3$

Evaluate expression without using a calculator. $\ln e ^ { 3 }$

Solve the equation. $\ln \left( x ^ { 2 } + 5 x \right) = \ln \left( x ^ { 2 } + 20 \right)$ If there is more than one solution, separate your answers with commas.

The quantity of a prescription drug in the bloodstream of a patient t hours after it is administered can be modeled by an exponential function. (See the graph.) Determine the time it takes to eliminate half of the initial dose from the body. __________ hr

Evaluate the expression. $5 ^ { \log _ { 5 } 8 }$

Determine whether the function is one-to-one. $f ( x ) = | 4 x |$ Answer yes or no .

If $\log _ { b } x ^ { 2 } = 1 + \log _ { b } 6$ , find b .

If $e ^ { \frac { t } { 6 } } = k ^ { t }$ find k .

Let $f ( x ) = 5 x - 4$ and $g ( x ) = x ^ { 2 } - 6$ . Find: f g

Determine the domain and range of the logarithmic function graphed below.

An isotope of thorium, ${ } ^ { 227 } \mathrm { Th }$ , has a half-life of 18.4 days. How long will it take for 77% of the sample to decompose? Please round the answer to the nearest tenth.

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 9: Exponential and Logarithmic Functions

Solve for x . log⁡8127=x\log _ { 81 } 27 = xlog81​27=x

Solve: log⁡8x=−13\log _ { 8 } x = - \frac { 1 } { 3 }log8​x=−31​

Does log⁡7log⁡6=log⁡7−log⁡6\frac { \log 7 } { \log 6 } = \log 7 - \log 6log6log7​=log7−log6 ? Answer yes or no .

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that h , j , k , and b are positive numbers, and log⁡59\log _ { 5 } 9log5​9 . log⁡b7=0.8451\log _ { b } 7 = 0.8451logb​7=0.8451

Write in logarithmic form: 42=164 ^ { 2 } = 1642=16

Let f(x)=3x−4f ( x ) = 3 x - 4f(x)=3x−4 and g(x)=x2−1g ( x ) = x ^ { 2 } - 1g(x)=x2−1 . Find: (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Write the logarithm as a difference. Then simplify, if possible. Assume that x is positive number. log⁡2x8\log _ { 2 } \frac { x } { 8 }log2​8x​

Solve: 3x2−3x=813 ^ { x ^ { 2 } - 3 x } = 813x2−3x=81

Evaluate the expression. log⁡93\log _ { 9 } 3log9​3

Evaluate expression without using a calculator. ln⁡e3\ln e ^ { 3 }lne3

Solve the equation. ln⁡(x2+5x)=ln⁡(x2+20)\ln \left( x ^ { 2 } + 5 x \right) = \ln \left( x ^ { 2 } + 20 \right)ln(x2+5x)=ln(x2+20) If there is more than one solution, separate your answers with commas.

The quantity of a prescription drug in the bloodstream of a patient t hours after it is administered can be modeled by an exponential function. (See the graph.) Determine the time it takes to eliminate half of the initial dose from the body. __________ hr

Evaluate the expression. 5log⁡585 ^ { \log _ { 5 } 8 }5log5​8

Determine whether the function is one-to-one. f(x)=∣4x∣f ( x ) = | 4 x |f(x)=∣4x∣ Answer yes or no .

If log⁡bx2=1+log⁡b6\log _ { b } x ^ { 2 } = 1 + \log _ { b } 6logb​x2=1+logb​6 , find b .

If et6=kte ^ { \frac { t } { 6 } } = k ^ { t }e6t​=kt find k .

Let f(x)=5x−4f ( x ) = 5 x - 4f(x)=5x−4 and g(x)=x2−6g ( x ) = x ^ { 2 } - 6g(x)=x2−6 . Find: f g

Determine the domain and range of the logarithmic function graphed below.

An isotope of thorium, 227Th{ } ^ { 227 } \mathrm { Th }227Th , has a half-life of 18.4 days. How long will it take for 77% of the sample to decompose? Please round the answer to the nearest tenth.

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Solve for x . $\log _ { 81 } 27 = x$

Solve: $\log _ { 8 } x = - \frac { 1 } { 3 }$

Does $\frac { \log 7 } { \log 6 } = \log 7 - \log 6$ ? Answer yes or no .

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that h , j , k , and b are positive numbers, and $\log _ { 5 } 9$ . $\log _ { b } 7 = 0.8451$

Write in logarithmic form: $4 ^ { 2 } = 16$

Let $f ( x ) = 3 x - 4$ and $g ( x ) = x ^ { 2 } - 1$ . Find: $( f \circ g ) ( x )$

Write the logarithm as a difference. Then simplify, if possible. Assume that x is positive number. $\log _ { 2 } \frac { x } { 8 }$

Solve: $3 ^ { x ^ { 2 } - 3 x } = 81$

Evaluate the expression. $\log _ { 9 } 3$

Evaluate expression without using a calculator. $\ln e ^ { 3 }$

Solve the equation. $\ln \left( x ^ { 2 } + 5 x \right) = \ln \left( x ^ { 2 } + 20 \right)$ If there is more than one solution, separate your answers with commas.

Evaluate the expression. $5 ^ { \log _ { 5 } 8 }$

Determine whether the function is one-to-one. $f ( x ) = | 4 x |$ Answer yes or no .

If $\log _ { b } x ^ { 2 } = 1 + \log _ { b } 6$ , find b .

If $e ^ { \frac { t } { 6 } } = k ^ { t }$ find k .

Let $f ( x ) = 5 x - 4$ and $g ( x ) = x ^ { 2 } - 6$ . Find: f g

An isotope of thorium, ${ } ^ { 227 } \mathrm { Th }$ , has a half-life of 18.4 days. How long will it take for 77% of the sample to decompose? Please round the answer to the nearest tenth.