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Solve for $x$ in.$$\frac{1}{8^{x+1}}=16^{1-4 x}$$

$$7 / 13$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

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Lectures

01:30

Solve.$$\left(\fra…

01:13

Solve for $x$ in.$$8^{…

01:28

Solve: $4^{x+1}=8^{x-1}$ <…

01:16

Solve for $x.$$$\left(…

01:34

Solve by any method.$$…

01:35

Solve.$$16\left(\f…

04:34

Find the value of $x^{\fra…

02:37

Solve the given equations.…

01:18

Solve equation.$4^{2 x…

So if we want to solve this, the first thing we're going to need to do is get a common denominator or not common denominator. Common factor on either side. So over here on the left, the first thing I'm going to do is actually rewrite this to where it is in the numerous posted it on there. So it's going to be eight now. It's going to be ready to the negative X plus one power and then on the right side, I'll just leave it as we have right now. Now we can go ahead and rewrite eight to be too cute, and then this is going to be raised to the negative X plus one power. Um, and actually, if I just distribute that negative, I'll just go ahead and do that. That would give negative X minus one. Now over here, 16 is two to the fourth power, and then that would be raised in the one minus four X. And now remember, when we have the power to a power, we multiply the powers so it will be too. Raise the three negative x minus one is able to to to the four times one minus four X like that and in this case is we have the same denominator. We can go ahead and not denominator base. I don't know why we can say that we can set the exponents equal, since the bases are the same and also distribute that three in that force. This give us negative three X minus three is 24 minus 16 x. So I'm going to add the 16 over. That's going to give us 13 X. I'm going to add the three over. That's going to give seven. And if I divide over by 13, that gives X is equal to 7/13, and so then this here should be our answer.

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