Logarithmic Functions
1. Write in logarithmic form. (a) \( 2^5=32 \)
(b) \( \left( \frac{1}{3}\right)^{-2}=9\)
solution
2. Convert to an exponential form. (a) \( \log_3 81 = 4 \)
(b) \(\log_a b = c \)
solution
3. Find the logarithm. (a) \(\log_5 \frac{1}{125} \) (b)
\(\log_8 2 \)
solution
4. Find the exact value of the logarithm. (a) \(\log_5 \sqrt[3] 5 \)
(b) \(\log_2(\log_3 81) \) (c) \(\log_5(\log_7 7) \)
solution
5. Solve the following equations.
(a) \(\log_2 (3x-1) = 3 \)
solution
(b)
\(\log_5(3x-2)=2 \) solution
(c) \( \log (x^2-7x+11) = 0 \)
solution
(d) \( \displaystyle{\log_3\left( \frac{x+1}{x-2}\right) = 1}\)
solution
6. Describe briefly how the graph of \(f(x)=\log_3(x-2) \) can be
obtained from the graph of \( y=\log_3 x\). Then graph the function and
find the domain, the vertical asymptote, x-intercept, and y-intercept.
solution
7. Find the domain of \( f(x)= \log \left( \frac{x-5}{x+2} \right)
\). solution