Solve the Natural Logarithm Equation: ln(4x) = Solution Steps

$\ln4x=$

To solve this problem, we’ll follow these steps:

• Step 1: Identify the expression $\ln 4x$.
• Step 2: Apply the change-of-base formula to transform the natural logarithm to one using base 7.
• Step 3: Use the formula $\ln a = \frac{\log_b a}{\log_b e}$ to substitute the values.

Now, let's work through each step:
Step 1: The expression given is $\ln 4x$.
Step 2: We want a base 7 logarithm, so we apply the change-of-base formula:
Step 3: We have:

$\ln 4x = \frac{\log_7 4x}{\log_7 e}$

Therefore, the logarithmic expression $\ln 4x$ in base 7 is equivalent to $\frac{\log_7 4x}{\log_7 e}$.

This matches the correct answer choice, which is choice 4.