We are asked to solve the equation $5(7)^x = 118$ for $x$ and round the answer to two decimal places.

1. Problem Description

We are asked to solve the equation $5(7)^x = 118$ for $x$ and round the answer to two decimal places.

2. Solution Steps

First, we divide both sides of the equation by 5:

$7^x = \frac{118}{5}$

$7^x = 23.6$

Now, we take the natural logarithm of both sides:

$\ln(7^x) = \ln(23.6)$

Using the power rule of logarithms, we have:

$x \ln(7) = \ln(23.6)$

Divide both sides by $\ln(7)$ to isolate $x$:

$x = \frac{\ln(23.6)}{\ln(7)}$

Now we can use a calculator to find the value of $x$:

$x \approx \frac{3.16156}{1.94591}$

$x \approx 1.6247$

Rounding to two decimal places, we get $x \approx 1.62$.

3. Final Answer

$x = 1.62$