Verified Answer :

altavistard

You haven't shared the possible answers, so the best I can do (which is very good!) is to assume we want to change from base 4 to base 10 and then apply the change of base formula.

Given log-to-the-base-4-of (x+2), we want log-to-the-base-10 of (x+2).  Following the change of base formula,
                                                log-to-the-base-4-of (x+2)
log-to-the-base-10 of (x+2) = ------------------------------------
                                                  log-to-the-base-4-of-10

Answer:  \(log_4(x+2)=\frac{log (x+2)}{log 4}\)

Step-by-step explanation:

By the log base formula,

\(log_b x = \frac{log_a x}{log_a b}\)

Where a and b are any numbers,

Here the given expression,

\(log_4(x+2)\)

Thus, by the above formula,

We can write,

\(log_4(x+2)=\frac{log_{10} (x+2)}{log_{10} 4 }\)

\(\implies log_4(x+2)=\frac{log(x+2)}{log 4}\)

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