Problems from Solving an exponential equation applying properties of the power

Solve the following exponential equation: $10^{\frac{3 x - 1}{2 x + 1}} = 100$

See development and solution

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

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

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

$x = - 3$

Hide solution and development

View theory