Question

how to find solution set of the equation:3^2+x=5^x?

Answer 1

Do you mean
\[3^2+x=5^x\Rightarrow 9+x=5^x?\]

Answer 2

@John_ES no, 2+x is actuallly exponent of \[3^2+^x=5^x\]

Answer 3

\[\log(3^{2+x})=\log(5^x)\Rightarrow (2+x)\log3=x\log5\Rightarrow x=\frac{2\log3}{\log5-\log3}\]
\[x=\frac{2\log3}{\log(5/3)}\approx4.3\]
The logs are decimal logarithms..