Question 1195399
<br>
{{{3^(2x-1)+2*3^(2x+1)=171}}}<br>
Make both exponents the same by rewriting {{{3^(2x+1)}}} as {{{(3^2)(3^(2x-1))}}}.<br>
{{{3^(2x-1)+2(3^2)(3^(2x-1))=171}}}
{{{3^(2x-1)+18*3^(2x-1)=171}}}
{{{19*3^(2x-1)=171}}}
{{{3^(2x-1)=171/19=9=3^2}}}
{{{2x-1=2}}}
{{{2x=3}}}
{{{x=3/2}}}<br>
ANSWER: x=3/2<br>
CHECK:
2x-1=3-1=2
2x+1=3+1=4
3^2+2*3^4=9+2(81)=9+162=171<br>