Find f(g(5) if f(x) = log x^2 and g(x) = x+5

Given the functions:

f(x) = log
x^2.

g(x) = x+ 5.

We need to find
f(g(5)).

First, we need to determine f(g(x)), then substitute with
x= 5

f(g(x))  = f( x+ 5) 

Now we will
substitute with x+ 5 in f(x):

==> f(g(x)) = log ( x+ 5)
^2

From logarithm properties we know
that:

log a^b = b*log a

==>
f(g(x)) = 2 * log (x+ 5)

==> f(g(x)) = 2*log(x+
5)

Now that we found f(g(x)) we will substitute with x=
5.

==> f(g(5)) = 2*log
(5+5)

                     = 2*log
10

But log 10 = 1

==> f(g(x)) =
2*1 = 2

==> f(g(5)) =
2