# A logarithm equation

Algebra Level 2

The value of $$\displaystyle{x}$$ that satisfies the equation $\log_{2}(2^{x-1} + 3^{x+1}) = 2x - \log_{2}(3^x)$ can be expressed as $$\displaystyle{\log_{a}b}$$. What is the value of $$\displaystyle{a+b}$$?

$$\quad$$ Note: $$a$$ and $$b$$ are both fractions and their sum is an integer.

×