Solve log₇4: Calculate the Base 7 Logarithm Value

To solve the problem of evaluating $\log_7 4$, we will use the change-of-base formula for logarithms.

The change-of-base formula is:

• $\log_b a = \frac{\log_k a}{\log_k b}$, where $k$ can be any base, commonly chosen as 10 (common logs) or $e$ (natural logs).

We will choose natural logarithms ($\ln$) for simplicity, therefore:

$\log_7 4 = \frac{\ln 4}{\ln 7}$

By applying the change-of-base formula, we find that the logarithm $\log_7 4$ can be expressed as $\frac{\ln 4}{\ln 7}$.

Upon examining the provided choices, we identify that choice 2: $\frac{\ln 4}{\ln 7}$ matches our result.

Therefore, the solution to the problem is $\frac{\ln 4}{\ln 7}$.