Question

Which expression results when the change of base formula is applied to log4 (x + 2)?

Answer 1

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 2

Answer:
`log_4(x+2)=(log (x+2))/(log 4)`

Explanation:

By the log base formula,

`log_b x = (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)=(log_(10) (x+2))/(log_(10) 4 )`

`\implies log_4(x+2)=(log(x+2))/(log 4)`