Question 54887
Solve:
{{{1/4 =8^(6x+5)}}}
{{{1/2^2=(2^3)^(6x+5)}}}
{{{2^(-2)=2^(3(6x+5))}}}  Since the bases are the same we can set the exponents = to each other.
{{{-2=3(6x+5)}}}
{{{-2=18x+15}}}
{{{-2-15=18x+15-15}}}
{{{-17=18x}}}
{{{-17/18=18x/18}}}
{{{highlight(x=-17/18)}}}
Another way to do it is to take log base 2 of both sides.  Let me know if you need to see it done that way.
Check:
{{{1/4=8^(6(-17/18)+5)}}}
{{{1/4=8^(-17/3+5)}}}
{{{1/4=8^(-17/3+15/3)}}}
{{{1/4=8^(-2/3)}}}
{{{1/4=(2^3)^(-2/3)}}}
{{{1/4=2^(3*-2/3)}}}
{{{1/4=2^(-2)}}}
{{{1/4=1/2^2}}}
{{{1/4=1/4}}}  We're right!!!
Happy Calculating!!!