3.4.1: Logarithms and Logarithmic Functions (Exercises)

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SECTION 5.4 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

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