Exponential and Logarithmic Equations

1. Solve each equation.   solution

(a) \( \displaystyle{4^{|x|} = 8}\)

(b) \( \displaystyle{\log_2(x+1) = 3}\)

(c) \( \displaystyle{\frac{1}{3}\log (x+1) - 1 = 0}\)

2. Solve each equation. Write the exact answer with natural logarithm and then approximate the result correct to three decimal places. 

(a) \(\displaystyle{ 2^{2x+3} = 15}\)    solution

(b) \(\displaystyle{ (\sqrt{5})^{x} = 8}\)    solution

(c) \(\displaystyle{ 2^{3x-1} = 7}\)    solution

(d) \(\displaystyle{ \frac{17}{5-3^x} = 6}\)    solution

3. Solve for x.  

(a) \(\displaystyle{ 1 + \log (3x - 4) = 0}\)   solution

(b) \(\displaystyle{ \log_2 (x^2-3x+2) = 1}\)   solution

(c) \(\displaystyle{ \log (x+8) + \log (x-1) = 1}\)   solution

(d) \(\displaystyle{ \log_4 x + \log_4 (x-6) = 2}\)   solution

(e) \(\displaystyle{ \log_3 (5x+2) - \log_3 (x-1) = 2}\)   solution

4. Solve the exponential equation.       \( 5^{2x} - 5^x -12 = 0 \)     solution