Solution
We can start taking common factor in both sides and we got:
[tex]3^x(1+3+3^2)=2^x(1+2^2+2^3)^{}[/tex]
and we can simplify like this:
[tex]3^x(13)=2^x(13)^{}[/tex]
We can cancel the 13 in both sides and we got:
[tex]3^x=2^x^{}[/tex]
Then we can do this using exponentials:
[tex]3^x-2^x=0^{}[/tex]
We got:
[tex]x\ln (3)=x\ln (2)[/tex]
then the only possible solution would be:
x=0
