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

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We have f(x) = log x^2 and g(x) = x+5.

To find f(g(5), we first find g(5)

g(x) = x+5

=> g(5) = 5 + 5

=> g(5) = 10

f(g(5)) = f(10).

f(x) = log x^2

=> f(10) = log 10^2

=> f(10) = log 100

=> f(x) = 2.

**Therefore f(g(5) = 2.**

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**

To find f(g(5)), if f(x) = logx^2. and g(x) = x+5.

f(x) = logx^2.

f(g(x)) = log((g(x))^2.

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

Put x= 5 on f(g(x)) = log(x+5)^2.

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

f(g(5))= log10^2 = 2.

f(g(5)) = 2.