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

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Answer 1 · 2018-06-18T21:26:25

$x=5/3$

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.

$=>10^(x-1)=10^(4x-6)$

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

$x-1=4x-6$

Subtracting $4x$ from both sides gives us

$-3x-1=-6$

Adding $1$ to both sides, we get

$-3x=-5$

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

$x=5/3$

Hope this helps!

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