Exam 9: Logarithmic and Exponential Functions

Graph. State the domain, range, and vertical asymptote of the function - $f(x)=\ln (x+1)-5$ $Graph. State the domain, range, and vertical asymptote of the function - f(x)=\ln (x+1)-5$

(Multiple Choice)

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Question 161

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log 17 x^{17}$

(Multiple Choice)

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Question 162

One interesting property of the function $f(x)=e^{x}$ is that its rate of change for any value $x$ is simply equal to $e^{x}$ . Find the rate of change of $f(x)=e^{x}$ for the given value of $x$ . Round to the nearest hundredth. - $x=-4$

(Multiple Choice)

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Question 163

Evaluate the given function - $f(x)=2^{-x}, f(5)$

(Multiple Choice)

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Question 164

$\left(\frac{2}{5}\right)^{x}=\frac{125}{8}$

(Multiple Choice)

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Question 165

One interesting property of the function $f(x)=e^{x}$ is that its rate of change for any value $x$ is simply equal to $e^{x}$ . Find the rate of change of $f(x)=e^{x}$ for the given value of $x$ . Round to the nearest hundredth. - $\mathrm{x}=6.7$

(Multiple Choice)

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Question 166

Determine whether function is one-to-one. -The function that pairs the radius of a spherical bowling ball with its volume.

(True/False)

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Question 167

Evaluate the given function. Round to the nearest thousandth. - $f(x)=e^{2 x-1}, f(-1)$

(Multiple Choice)

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Question 168

Solve. - $\log _{2}(x-2)=-1$

(Multiple Choice)

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Question 169

Solve. Round to the nearest thousandth. - $\mathrm{e}^{2 \mathrm{x}}-20 \mathrm{e}^{\mathrm{x}}+91=0$

(Multiple Choice)

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Question 170

Evaluate the given function. - $f(x)=\log _{2} x, f(8)$

(Multiple Choice)

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Question 171

Solve the problem. -The function $\mathrm{w}(\mathrm{x})=5 \mathrm{x}-3$ describes a company's monthly costs in wages and $\mathrm{p}(\mathrm{x})=2 \mathrm{x}-9$ describes the cost of production, where $x$ represents the number of units produced. Find the function $\mathrm{c}(\mathrm{x})$ that describes the total cost of producing $\mathrm{x}$ units.

(Multiple Choice)

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Question 172

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers. - $\log _{13}\left(\frac{14 m}{n}\right)$

(Multiple Choice)

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Question 173

Simplify. - $e^{\ln 0.327}$

(Multiple Choice)

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Question 174

Evaluate the given function. - $f(x)=16 \log _{2}(3 x), f\left(\frac{1}{12}\right)$

(Multiple Choice)

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Question 175

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _{3} \sqrt[4]{\mathrm{z}}$

(Multiple Choice)

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Question 176

For the given logarithmic function, find a) the average rate of change for the interval $[2,6]$ and b) the interval $[3,5]$ , as well as $c$ ) the rate of change at $x=4$ . Round all calculations to the nearest thousandth. - $f(x)=\log (x+1.5)+32.9$

(Multiple Choice)

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Question 177

Find the specified domain -For $f(x)=2 x-5$ and $g(x)=\sqrt{x+2}$ , what is the domain of $g$ of?

(Multiple Choice)

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Question 178

Solve. -Susan purchased a painting in the year 2000 for $\$ 7000$ . Assuming an exponential rate of inflation of $2.9 \%$ per year, how much will the painting be worth 8 years later?

(Multiple Choice)

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Question 179

Solve. - $2-x=\frac{1}{8}$

(Multiple Choice)

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Question 180

Graph. State the domain, range, and vertical asymptote of the function - $f(x)=\ln (x+1)-5$ $Graph. State the domain, range, and vertical asymptote of the function - f(x)=\ln (x+1)-5$

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log 17 x^{17}$

One interesting property of the function $f(x)=e^{x}$ is that its rate of change for any value $x$ is simply equal to $e^{x}$ . Find the rate of change of $f(x)=e^{x}$ for the given value of $x$ . Round to the nearest hundredth. - $x=-4$

Evaluate the given function - $f(x)=2^{-x}, f(5)$

$\left(\frac{2}{5}\right)^{x}=\frac{125}{8}$

One interesting property of the function $f(x)=e^{x}$ is that its rate of change for any value $x$ is simply equal to $e^{x}$ . Find the rate of change of $f(x)=e^{x}$ for the given value of $x$ . Round to the nearest hundredth. - $\mathrm{x}=6.7$

Determine whether function is one-to-one. -The function that pairs the radius of a spherical bowling ball with its volume.

Evaluate the given function. Round to the nearest thousandth. - $f(x)=e^{2 x-1}, f(-1)$

Solve. - $\log _{2}(x-2)=-1$

Solve. Round to the nearest thousandth. - $\mathrm{e}^{2 \mathrm{x}}-20 \mathrm{e}^{\mathrm{x}}+91=0$

Evaluate the given function. - $f(x)=\log _{2} x, f(8)$

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers. - $\log _{13}\left(\frac{14 m}{n}\right)$

Simplify. - $e^{\ln 0.327}$

Evaluate the given function. - $f(x)=16 \log _{2}(3 x), f\left(\frac{1}{12}\right)$

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _{3} \sqrt[4]{\mathrm{z}}$

For the given logarithmic function, find a) the average rate of change for the interval $[2,6]$ and b) the interval $[3,5]$ , as well as $c$ ) the rate of change at $x=4$ . Round all calculations to the nearest thousandth. - $f(x)=\log (x+1.5)+32.9$

Find the specified domain -For $f(x)=2 x-5$ and $g(x)=\sqrt{x+2}$ , what is the domain of $g$ of?

Solve. -Susan purchased a painting in the year 2000 for $\$ 7000$ . Assuming an exponential rate of inflation of $2.9 \%$ per year, how much will the painting be worth 8 years later?

Solve. - $2-x=\frac{1}{8}$

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

Graph. State the domain, range, and vertical asymptote of the function - f(x)=ln⁡(x+1)−5f(x)=\ln (x+1)-5f(x)=ln(x+1)−5

Rewrite using the power rule. Assume all variables represent positive real numbers. - log⁡17x17\log 17 x^{17}log17x17

One interesting property of the function f(x)=exf(x)=e^{x}f(x)=ex is that its rate of change for any value xxx is simply equal to exe^{x}ex . Find the rate of change of f(x)=exf(x)=e^{x}f(x)=ex for the given value of xxx . Round to the nearest hundredth. - x=−4x=-4x=−4

Evaluate the given function - f(x)=2−x,f(5)f(x)=2^{-x}, f(5)f(x)=2−x,f(5)

(25)x=1258\left(\frac{2}{5}\right)^{x}=\frac{125}{8}(52​)x=8125​

One interesting property of the function f(x)=exf(x)=e^{x}f(x)=ex is that its rate of change for any value xxx is simply equal to exe^{x}ex . Find the rate of change of f(x)=exf(x)=e^{x}f(x)=ex for the given value of xxx . Round to the nearest hundredth. - x=6.7\mathrm{x}=6.7x=6.7

Determine whether function is one-to-one. -The function that pairs the radius of a spherical bowling ball with its volume.

Evaluate the given function. Round to the nearest thousandth. - f(x)=e2x−1,f(−1)f(x)=e^{2 x-1}, f(-1)f(x)=e2x−1,f(−1)

Solve. - log⁡2(x−2)=−1\log _{2}(x-2)=-1log2​(x−2)=−1

Solve. Round to the nearest thousandth. - e2x−20ex+91=0\mathrm{e}^{2 \mathrm{x}}-20 \mathrm{e}^{\mathrm{x}}+91=0e2x−20ex+91=0

Evaluate the given function. - f(x)=log⁡2x,f(8)f(x)=\log _{2} x, f(8)f(x)=log2​x,f(8)

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers. - log⁡13(14mn)\log _{13}\left(\frac{14 m}{n}\right)log13​(n14m​)

Simplify. - eln⁡0.327e^{\ln 0.327}eln0.327

Evaluate the given function. - f(x)=16log⁡2(3x),f(112)f(x)=16 \log _{2}(3 x), f\left(\frac{1}{12}\right)f(x)=16log2​(3x),f(121​)

Rewrite using the power rule. Assume all variables represent positive real numbers. - log⁡3z4\log _{3} \sqrt[4]{\mathrm{z}}log3​4z​

Find the specified domain -For f(x)=2x−5f(x)=2 x-5f(x)=2x−5 and g(x)=x+2g(x)=\sqrt{x+2}g(x)=x+2​ , what is the domain of ggg of?

Solve. -Susan purchased a painting in the year 2000 for $7000\$ 7000$7000 . Assuming an exponential rate of inflation of 2.9%2.9 \%2.9% per year, how much will the painting be worth 8 years later?

Solve. - 2−x=182-x=\frac{1}{8}2−x=81​

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

Graph. State the domain, range, and vertical asymptote of the function - $f(x)=\ln (x+1)-5$ $Graph. State the domain, range, and vertical asymptote of the function - f(x)=\ln (x+1)-5$

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log 17 x^{17}$

One interesting property of the function $f(x)=e^{x}$ is that its rate of change for any value $x$ is simply equal to $e^{x}$ . Find the rate of change of $f(x)=e^{x}$ for the given value of $x$ . Round to the nearest hundredth. - $x=-4$

Evaluate the given function - $f(x)=2^{-x}, f(5)$

$\left(\frac{2}{5}\right)^{x}=\frac{125}{8}$

One interesting property of the function $f(x)=e^{x}$ is that its rate of change for any value $x$ is simply equal to $e^{x}$ . Find the rate of change of $f(x)=e^{x}$ for the given value of $x$ . Round to the nearest hundredth. - $\mathrm{x}=6.7$

Evaluate the given function. Round to the nearest thousandth. - $f(x)=e^{2 x-1}, f(-1)$

Solve. - $\log _{2}(x-2)=-1$

Solve. Round to the nearest thousandth. - $\mathrm{e}^{2 \mathrm{x}}-20 \mathrm{e}^{\mathrm{x}}+91=0$

Evaluate the given function. - $f(x)=\log _{2} x, f(8)$

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers. - $\log _{13}\left(\frac{14 m}{n}\right)$

Simplify. - $e^{\ln 0.327}$

Evaluate the given function. - $f(x)=16 \log _{2}(3 x), f\left(\frac{1}{12}\right)$

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _{3} \sqrt[4]{\mathrm{z}}$

Find the specified domain -For $f(x)=2 x-5$ and $g(x)=\sqrt{x+2}$ , what is the domain of $g$ of?

Solve. -Susan purchased a painting in the year 2000 for $\$ 7000$ . Assuming an exponential rate of inflation of $2.9 \%$ per year, how much will the painting be worth 8 years later?

Solve. - $2-x=\frac{1}{8}$