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7.3E: Exercises - Logarithms and Logarithmic Functions

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    PROBLEM SET: LOGARITHMS AND LOGARITHMIC FUNCTIONS

    Rewrite each of these exponential expressions in logarithmic form:

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

    Rewrite each of these logarithmic expressions in exponential form:

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

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

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

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

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

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

    Evaluate without using your calculator.

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

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

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

    7.3E: Exercises - Logarithms and Logarithmic Functions is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by LibreTexts.