Explanation;
To solve an exponential Equation with different bases we need to the following steps;
1. Isolate the exponential part of the equation. If there are two exponential parts put one on each side of the equation.
2^x=3^x+1
2. Introduce logarithm of each side of the equation;
log 2^x = log 3^x+1
3. Then apply power property to rewrite the exponent.
x log 2= (x+1)log 3
4. Then Solve for the variable ;
x log 2 = log 3 + x log 3
x log 2 - x log 3 = log 3
x (log 2 - log 3) = log 3
and x = log 3 / (log 3 - log 2)
