Use the natural logarithm to solve the given equation. Round to the nearest ten-thousandth.

Answer:
-0.8340
Step-by-step explanation:
After changing the exponential function to logarithm plot the log equation into the calculator to find the answer
3^x = 0.4 is changed to log_3 (0.4)
Answer:
[tex]x \: \: \: is \: approx \: \: \: - 0.8340[/tex]
Step-by-step explanation:
[tex] {3}^{x} = .4 \\ .4 = \frac{4}{10} = \frac{2}{5} [/tex]
[tex] {3}^{x} = \frac{2}{5 } \\ ln( {3}^{x} ) = ln( \frac{2}{5} ) \\ x ln(3) = ln( \frac{2}{5} ) \\ x = \frac{ ln( \frac{2}{5} ) }{ ln(3) } = - 0.8340[/tex]