Problems from Solving an exponential equation applying properties of the power

Development:

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

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

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

Solution:

$$x=-3$$

Hide solution and development