# How do you solve 10^(x-1)=100^(2x-3)?

Jun 18, 2018

$x = \frac{5}{3}$

#### Explanation:

Let's rewrite the right side in terms of base-$10$. This gives us

10^(x-1)=color(blue)(10^((2)*(2x-3))

Notice, ${10}^{2} = 100$, so we didn't change the value of the equation.

$\implies {10}^{x - 1} = {10}^{4 x - 6}$

Since we have the same bases, the exponents are equivalent. We can now set up the following equation:

$x - 1 = 4 x - 6$

Subtracting $4 x$ from both sides gives us

$- 3 x - 1 = - 6$

Adding $1$ to both sides, we get

$- 3 x = - 5$

Lastly, dividing both sides by $- 3$, we get

$x = \frac{5}{3}$

Hope this helps!