Question 371060
{{{15^x=5^(x+2)}}}
<pre>
Take logs of both sides

{{{log(15^x)=log(5^(x+2))}}}

{{{x*log(15)=(x+2)log(5)}}}

{{{x*log(15)=x*log(5)+2*log(5)}}}

Get both terms that contain x alone on the left.

{{{x*log(15)-x*log(5)=2*log(5)}}}

Factor out x

{{{x(log(15)-log(5))=2*log(5)}}}

Divide both sides by that big parentheses:

{{{x=(2*log(5))/(log(15)-log(5)) }}}

You can get the numerical approximation from that 
or you can simplify some more.

{{{x=(2*log(5))/log(15/5) }}}

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

{{{x=2.929947041}}}

Edwin</pre>