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Solve for $x$ in.$$16^{3 x+1}=64^{2-5 x}$$

$$4 / 21$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Campbell University

University of Michigan - Ann Arbor

Idaho State University

Lectures

02:50

Solve each equation.$$…

00:43

00:50

00:41

Solve equation.$2^{5 x…

01:17

Solve for $x$.$$4^…

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02:09

01:13

Solve for $x$ in.$$8^{…

01:04

Solve for $x$.$$\left(…

02:23

00:56

00:19

So if we want to solve this, the first thing we need to do is get a common base. Um, you could do to, but the one that actually jumps out to me is going to be four because 16 is four squared, 64 is for cubed, and then we still have our powers. So three X plus one and then two minus five X like that. Um, if you do, the power of two will end up working out to give you the same answer. Regardless of I just think doing it this way. We'll give a slightly smaller numbers to work with in the end. But now we have the power to a power. We just multiply the power. So it would be four times two or four races the two times three X plus one, and it's going to be equal to four races three times two minus five x. So now we can go ahead and set these powers equal to each other. Since our bases are the same and I'm going to distribute the two and the three wall of Minnesota V six x Boston, and this is going to be able to six minus 15 x. So first, I'm going to add the 15 x over. So it gives me 21 x on the left side. Subtract the two. That would give us a four divide over by 21. So we get X is equal to 4/21. So this here should be our solution.

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