Question 873015
<pre>
You might find it easier to use substitution of
a logarithm by a letter to keep from getting
bogged down in the notation.

{{{5^(x+2)}}}{{{""=""}}}{{{3^(x)}}}

Take logs of both sides

{{{log((5^(x+2)))}}}{{{""=""}}}{{{log((3^(x)))}}}

Use this rule:

"The logarithm of an exponential number is the 
exponent times the logarithm of the base."

(x+2)log(5) = x*log(3)

Now substitute the letter A for log(5) and B for  log(3)

(x+2)A = xB

A(x+2) = Bx

Ax+2A = Bx

Ax-Bx = -2A

x(A-B) = -2A

x = {{{-2A/(A-B)}}}

Now replace the letter A by log(5) 
and the letters B by log(3) 

x = {{{-2log((5))/(log(5)-log(3))}}}

Then take a calculator and find x = -6.301320206

Edwin</pre>