Checkpoint: Solve Natural Logarithms Solution

Solve using natural logarithms.

$7^{0.3 x} = 712$

$\ln 7^{0.3 x} = \ln 712 (0.3 x) \ln 7 = \ln 712 0.3 x = \frac{\ln 712}{\ln 7} (\frac{10}{3}) \frac{3}{10} x = \frac{\ln 712}{\ln 7} (\frac{10}{3}) x = \frac{10 \ln 712}{3 \ln 7}$

Note

Q: What is the first step in solving this equation?
A: Rewrite the numbers on both sides as natural logs.

To check the solution, substitute the value of x into the original equation.