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

Mar 8, 2017

$x = 1$

#### Explanation:

Express the exponential on the right side with a $\textcolor{b l u e}{\text{base of 10}}$

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

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

Since the bases on both sides are 10 then equate the exponents.

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

$\Rightarrow 7 x = 7$

$\Rightarrow x = 1 \text{ is the solution}$