Question

find the logarithm log4(256)

Answer 1

154.12735778

Answer 2

Power rule will make it simple.

Answer 3

\[\log_4(256)\]

Answer 4

And the power rule says:
\[\log(a)^m = m \log(a)\]

Answer 5

So, you can write \(256\) as \(4^4\)

Answer 6

\[\log_4(256) = \log_4(4)^4 \implies \color{green}{4} \log_4(4)\]

Answer 7

and one more thing:
\[\log_a(a) = 1\]

Answer 8

So:
\[\log_4(4) = 1\]

Answer 9

So, at last you have:
\[\color{blue}{\log_4(256) = 4}\]