Exam 10: Inverse, Exponential, and Logarithmic Functions

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 . - $\log _{5} 7-\log _{5} z$

(Multiple Choice)

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Question 41

Solve the equation. Give the solution to three decimal places. - $6 x+1=28$

(Multiple Choice)

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Question 42

Solve the problem. Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm{pH}=-\log \left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ , as needed. -Find the $\mathrm{pH}$ if $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-1}$ .

(Multiple Choice)

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Question 43

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - $\mathrm{e}^{-0.416 \mathrm{x}}=26$

(Multiple Choice)

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Question 44

Decide whether each function is one-to-one -(i) $f(x)=x^{2}-4$ (ii) $Decide whether each function is one-to-one -(i) f(x)=x^{2}-4 (ii)$

(Multiple Choice)

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Question 45

Solve the equation. Give the solution to three decimal places. - $3^{-x-1}=10$

(Multiple Choice)

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Question 46

Solve the equation. Give the solution to three decimal places. - $4^{3 x}=5^{x+1}$

(Multiple Choice)

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Question 47

Use the horizontal line test to determine if the function is one-to-one. -

(True/False)

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Question 48

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x)=8 x^{2}-4$

(Multiple Choice)

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Question 49

Find the logarithm. Give an approximation to four decimal places - $\ln 0.990$

(Multiple Choice)

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Question 50

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. - $\log _{3} \frac{\sqrt[4]{\mathrm{m}} \sqrt[5]{\mathrm{n}}}{\mathrm{k}^{2}}$

(Multiple Choice)

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Question 51

Solve the equation. Give the exact solution or solutions. - $\log (x+3)=\log (5 x-1)$

(Multiple Choice)

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Question 52

Find the amount of money in an account after 12 years if $\$ 1900$ is deposited at $7 \%$ annual interest compounded annually.

(Multiple Choice)

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Question 53

Solve the equation. Give the exact solution - $9^{x}=81(3 x-3)$

(Multiple Choice)

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Question 54

Write in exponential form. - $\log _{x} 243=5$

(Multiple Choice)

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Question 55

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - $\mathrm{e}^{\ln (6-\mathrm{x})}=\mathrm{e}^{\ln (2+4 \mathrm{x})}$

(Multiple Choice)

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Question 56

Evaluate the logarithm. - $\log _{5}\left(\frac{1}{25}\right)$

(Multiple Choice)

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Question 57

Find the logarithm. Give an approximation to four decimal places. - $\ln 0.989$

(Multiple Choice)

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Question 58

$\log _{5} 5^{-1}+\log _{5} 5=0$

(True/False)

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Question 59

Write in exponential form. - $\log _{8} x=\frac{1}{3}$

(Multiple Choice)

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Question 60

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 . - $\log _{5} 7-\log _{5} z$

Solve the equation. Give the solution to three decimal places. - $6 x+1=28$

Solve the problem. Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm{pH}=-\log \left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ , as needed. -Find the $\mathrm{pH}$ if $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-1}$ .

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - $\mathrm{e}^{-0.416 \mathrm{x}}=26$

Decide whether each function is one-to-one -(i) $f(x)=x^{2}-4$ (ii) $Decide whether each function is one-to-one -(i) f(x)=x^{2}-4 (ii)$

Solve the equation. Give the solution to three decimal places. - $3^{-x-1}=10$

Solve the equation. Give the solution to three decimal places. - $4^{3 x}=5^{x+1}$

Use the horizontal line test to determine if the function is one-to-one. -

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x)=8 x^{2}-4$

Find the logarithm. Give an approximation to four decimal places - $\ln 0.990$

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. - $\log _{3} \frac{\sqrt[4]{\mathrm{m}} \sqrt[5]{\mathrm{n}}}{\mathrm{k}^{2}}$

Solve the equation. Give the exact solution or solutions. - $\log (x+3)=\log (5 x-1)$

Find the amount of money in an account after 12 years if $\$ 1900$ is deposited at $7 \%$ annual interest compounded annually.

Solve the equation. Give the exact solution - $9^{x}=81(3 x-3)$

Write in exponential form. - $\log _{x} 243=5$

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - $\mathrm{e}^{\ln (6-\mathrm{x})}=\mathrm{e}^{\ln (2+4 \mathrm{x})}$

Evaluate the logarithm. - $\log _{5}\left(\frac{1}{25}\right)$

Find the logarithm. Give an approximation to four decimal places. - $\ln 0.989$

$\log _{5} 5^{-1}+\log _{5} 5=0$

Write in exponential form. - $\log _{8} x=\frac{1}{3}$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 10: Inverse, Exponential, and Logarithmic Functions

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 . - log⁡57−log⁡5z\log _{5} 7-\log _{5} zlog5​7−log5​z

Solve the equation. Give the solution to three decimal places. - 6x+1=286 x+1=286x+1=28

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - e−0.416x=26\mathrm{e}^{-0.416 \mathrm{x}}=26e−0.416x=26

Decide whether each function is one-to-one -(i) f(x)=x2−4f(x)=x^{2}-4f(x)=x2−4 (ii)

Solve the equation. Give the solution to three decimal places. - 3−x−1=103^{-x-1}=103−x−1=10

Solve the equation. Give the solution to three decimal places. - 43x=5x+14^{3 x}=5^{x+1}43x=5x+1

Use the horizontal line test to determine if the function is one-to-one. -

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - f(x)=8x2−4f(x)=8 x^{2}-4f(x)=8x2−4

Find the logarithm. Give an approximation to four decimal places - ln⁡0.990\ln 0.990ln0.990

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. - log⁡3m4n5k2\log _{3} \frac{\sqrt[4]{\mathrm{m}} \sqrt[5]{\mathrm{n}}}{\mathrm{k}^{2}}log3​k24m​5n​​

Solve the equation. Give the exact solution or solutions. - log⁡(x+3)=log⁡(5x−1)\log (x+3)=\log (5 x-1)log(x+3)=log(5x−1)

Find the amount of money in an account after 12 years if $1900\$ 1900$1900 is deposited at 7%7 \%7% annual interest compounded annually.

Solve the equation. Give the exact solution - 9x=81(3x−3)9^{x}=81(3 x-3)9x=81(3x−3)

Write in exponential form. - log⁡x243=5\log _{x} 243=5logx​243=5

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - eln⁡(6−x)=eln⁡(2+4x)\mathrm{e}^{\ln (6-\mathrm{x})}=\mathrm{e}^{\ln (2+4 \mathrm{x})}eln(6−x)=eln(2+4x)

Evaluate the logarithm. - log⁡5(125)\log _{5}\left(\frac{1}{25}\right)log5​(251​)

Find the logarithm. Give an approximation to four decimal places. - ln⁡0.989\ln 0.989ln0.989

log⁡55−1+log⁡55=0\log _{5} 5^{-1}+\log _{5} 5=0log5​5−1+log5​5=0

Write in exponential form. - log⁡8x=13\log _{8} x=\frac{1}{3}log8​x=31​

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 . - $\log _{5} 7-\log _{5} z$

Solve the equation. Give the solution to three decimal places. - $6 x+1=28$

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - $\mathrm{e}^{-0.416 \mathrm{x}}=26$

Decide whether each function is one-to-one -(i) $f(x)=x^{2}-4$ (ii) $Decide whether each function is one-to-one -(i) f(x)=x^{2}-4 (ii)$

Solve the equation. Give the solution to three decimal places. - $3^{-x-1}=10$

Solve the equation. Give the solution to three decimal places. - $4^{3 x}=5^{x+1}$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x)=8 x^{2}-4$

Find the logarithm. Give an approximation to four decimal places - $\ln 0.990$

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. - $\log _{3} \frac{\sqrt[4]{\mathrm{m}} \sqrt[5]{\mathrm{n}}}{\mathrm{k}^{2}}$

Solve the equation. Give the exact solution or solutions. - $\log (x+3)=\log (5 x-1)$

Find the amount of money in an account after 12 years if $\$ 1900$ is deposited at $7 \%$ annual interest compounded annually.

Solve the equation. Give the exact solution - $9^{x}=81(3 x-3)$

Write in exponential form. - $\log _{x} 243=5$

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - $\mathrm{e}^{\ln (6-\mathrm{x})}=\mathrm{e}^{\ln (2+4 \mathrm{x})}$

Evaluate the logarithm. - $\log _{5}\left(\frac{1}{25}\right)$

Find the logarithm. Give an approximation to four decimal places. - $\ln 0.989$

$\log _{5} 5^{-1}+\log _{5} 5=0$

Write in exponential form. - $\log _{8} x=\frac{1}{3}$