# How do you solve 10^(x-3)=100^(4x-5)?

Sep 21, 2016

$x = 1$

#### Explanation:

We have: ${10}^{x - 3} = {100}^{4 x - 5}$

Let's express both sides of the equation in terms of $10$:

$\implies {10}^{x - 3} = {\left({10}^{2}\right)}^{4 x - 5}$

Using the laws of exponents:

$\implies {10}^{x - 3} = {10}^{8 x - 10}$

$\implies x - 3 = 8 x - 10$

$\implies 7 x = 7$

$\implies x = 1$

Therefore, the solution to the equation is $x = 1$.