Question 863620
{{{9^(x^2)=27^(x+3)}}}
{{{(3^2)^(x^2)=(3^3)^(x+3)}}}
{{{(3)^(2x^2)=(3)^(3(x+3))}}}
{{{2x^2=3(x+3)}}}
{{{2x^2=3x+9}}}
{{{(x-3)(2x+3)=0}}}
Two solutions:
{{{x-3=0}}}
{{{x=3}}}
and
{{{2x+3=0}}}
{{{2x=-3}}}
{{{x=-3/2}}}
.
.
.
{{{log(2x+1)=1-log(x-1)}}}
{{{log(2x+1)+log(x-1)=1}}}
{{{log((2x+1)(x-1))=1}}}
{{{(2x+1)(x-1)=10}}}
{{{2x^2-2x+x-1=10}}}
{{{2x^2-x-11=0}}}
{{{2(x^2-x/2)=11}}}
{{{2(x^2-x/2+1/16)=11+1/8}}}
{{{2(x-1/4)^2=89/8}}}
{{{(x-1/4)^2=89/16}}}
{{{x-1/4=0 +- sqrt(89)/4}}}
{{{x=1/4 +- sqrt(89)/4}}}
Since (2x+1) is the argument of a log function, {{{2x+1>0}}} or {{{x>-1/2}}}, so we will ignore the negative solution.
{{{x=1/4+sqrt(89)/4}}}
{{{x=(1+sqrt(89))/4}}}