Solving an exponential equation applying properties of the power

$$10^{\frac{3x-1}{2x+1}}=100$$

We reduce to the same basis and obtain $$10^{\frac{3x-1}{2x+1}}=10^2$$

Then, equalling exponents, we get $$\dfrac{3x-1}{2x+1}=2 \Rightarrow 3x-1=4x+2 \Rightarrow x=-3$$