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Solve for $x$ in.$$8^{2 x-3}=16^{1-4 x}$$

$$13 / 22$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

McMaster University

University of Michigan - Ann Arbor

Lectures

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02:36

01:01

So if we want to solve these, uh, first we're gonna need to go ahead and get a common denominator or not commenting on common base. So eight becomes too cute, 16 becomes two to the fourth, and then we can just leave everything else as it was. And then remember, whenever we have a power to a power, we multiply the powers. It would be too todd or two to the three times two X minus three, and then this is going to be equal to to to the four times one minus four X. Now, since these have the same base, we can set the exponents even to each other. And then while we're at it, I'm just going to distribute, um, those numbers out front. So on the left side, that's going to become six x minus. Die on the right side is going to become for my 16 X. Now I can add the 16 x over, so that gives me 22 x Add the dying over. That gives me 13. Divide by 2020 side and we'll end up FX 0 to 13/22. And so than this is going to be our solution

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