Section 3.2: Logarithmic Functions

  1. Express the equation in exponential form.   solution

    2. (a) $\log_{27}(3)=\frac{1}{3}$   (b) \(\log_{1/5}(7y)=4 \)   (c) $\ln(5)=2y$   (d) $\ln(t+2) = -1$

  2. Express the equation in logarithmic form.   solution

    3. (a) $10^{-2}=\frac{1}{100}$   (b) $5^{3x}=10$   (c) $e^{x+2}=0.6$   (d) $e^{0.9x}=t$

  3. Evaluate the epression using properties of logarithm.   solution

    4. (a) $\log_3 \left( \frac{1}{243}\right)$   (b) $\log_{1/4}(64)$   (c) $\log_4(\sqrt{4})$   (d) $\ln(e^3)$   (e) $\ln(1/e)$  

  4. Evaluate the expression using properties of logarithm.   solution

    5. (a) $\log_4(0.125)$   (b) $\log_4(\sqrt{2})$   (c) $\log_4\left(\frac{1}{2} \right) $   (d) $\log_4(8)$

  5. Find the exact value of the logarithm.    solution

    6. (a) \(\log_5 \sqrt[3] 5 \) (b) \(\log_2(\log_3 81) \)   (c) \(\log_5(\log_7 7) \)

  6. Solve for $x$.   solution

    7. (a) $\log_2(x)=4$   (b) $\ln(1/e)=x$   (c) $\ln(5x+6)=3 $   (d) $5 \log_{10}(x-3)=12$

  7. Use the Change of Base formula and a calculator to evaluate the logarithm.   solution

    8. (a) $\log_6(3)$   (b) $\log_8(96)$   (c) $\log_4(7)$