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

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Answer 1 · 2016-09-21T21:31:35

$x = 1$

We have: $10^(x - 3) = 100^(4 x - 5)$

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

$=> 10^(x - 3) = (10^(2))^(4 x - 5)$

Using the laws of exponents:

$=> 10^(x - 3) = 10^(8 x - 10)$

$=> x - 3 = 8 x - 10$

$=> 7 x = 7$

$=> x = 1$

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

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