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Solve for $x$ in.$$\frac{2^{3 x} 4^{2 x-1}}{8^{2+3 x}}=16^{3 x+7}$$

$$-18 / 7$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

McMaster University

Baylor University

Idaho State University

Lectures

02:17

Solve the equation.$$4…

01:13

Solve for $x$ in.$$8^{…

01:46

Solve for $x$. $$4…

01:30

Solve for $x.$$$\frac{…

02:53

Solve for $x.$$$4^{x+2…

02:15

Solve.$$\frac{x}{x^{2}…

01:27

Solve for $x$.$$4^…

00:31

Solve equation.$4^{2 x…

01:18

01:09

Solve.$\frac{3}{4} x^{…

01:01

Solve for $x.$$$4^{3}=…

04:30

Solve the equations for $x…

If we want to go ahead and solve this, the first thing I would do is go ahead and try to get a common base on either side. So on the left side, um, this is going to give us just 2 to 3 X, and then four is going to become two squared. That's raised to express one. Uh, and what I'm going to do is I'm just going to multiply this over to the right side. Um, and then over here, this is going to be 16 is going to be two to the fourth, raised to three X plus seven and then eight is supposed to be in here. I'll write this in blue, just kind of show. I've moved it over too cute. Raised the two x, not two x two plus three acts. All right. Now, the first thing we can go ahead and do is, um, use the fact that we know if we have a power to a power, we just multiply the powers. Uh, and then once we have that, we can go ahead and, um, add the power since we're multiplying things on either side. So over here, this would be two times two x minus one. So that would give us four X minus two over here. That would give us two. So four times three would be 12 x times 7 28 and then times two and then three times to six plus nine X. Then remember, we can add the powers on each side since we're multiplying. So it would be seven x minus two on the left. And then over here it would be still 12 x plus my next 21 x and then 28 6 would be 34. And now that we have a common based on either side, we can just go ahead and set the powers equal. It would be seven Express to was able to 21 x plus 34. So I'm going to subtract seven over. So be 14 X and then I'm going to subtract 34 so that would be negative. 36. Then we can go ahead and divide 14 on each side would be negative. 36/14, um, and 36/14 should simplify down to 18/7. So this is going to be X is equal to negative. 18/7

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