5.3E: Exercises - Logarithms and Logarithmic Functions

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Mar 6, 2024
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- 5.3: Logarithms and Logarithmic Functions
- 5.4: Graphs and Properties of Logarithmic Functions

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PROBLEM SET: LOGARITHMS AND LOGARITHMIC FUNCTIONS

Rewrite each of these exponential expressions in logarithmic form:

$3^{4}=81$	$10^{5}=100,000$
$5^{-2}=0.04$	$4^{-1}=0.25$
$16^{1 / 4}=2$	$9^{1 / 2}=3$

Rewrite each of these logarithmic expressions in exponential form:

$\log _{5} 625=4$	$\log _{2}(1 / 32)=-5$
$\log _{11} 1331=3$	$\log _{10} 0.0001=-4$
$\log _{64} 4=1 / 3$	$\ln \sqrt{e}=\frac{1}{2}$

If the expression is in exponential form, rewrite it in logarithmic form.

If the expression is in logarithmic form, rewrite it in exponential form.

$5^{x}=15625$	$x=9^{3}$
$\log _{5} 125=x$	$\log _{3} x=5$
$\log _{10} y=4$	$\mathrm{e}^{\mathrm{x}}=10$
$\ln x=-1$	$e^{5}=y$

For each equation, rewrite in exponential form and solve for x.

$\log _{5}(x)=3$	$\log _{2}(x)=-2$
$\log _{10}(x)=-3$	$\log _{3}(x)=6$
$\log _{25}(x)=1 / 2$	$\log _{64}(x)=1 / 3$

Evaluate without using your calculator.

$\ln \sqrt[3]{e}$	$\ln \frac{1}{e^{2}}$
$\ln \mathrm{e}^{10}$	$\log _{10}\left(10^{e}\right)$

For problems 31 – 38: Evaluate using your calculator. Use the change of base formula if needed

$\log 20$	$\ln 42$
$\ln 2.9$	$\log 0.5$
$\log _{4} 36$	$\log _{7} 100$
$\log _{105} 3.5$	$\log _{1.067} 2$

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PROBLEM SET: LOGARITHMS AND LOGARITHMIC FUNCTIONS

PROBLEM SET: LOGARITHMS AND LOGARITHMIC FUNCTIONS

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