Question

Solve and check.
4^2x= 32^1/2
Can someone walk me through the steps? Thank you!! :)

Answer 1

32 to the power of 1/2

Answer 2

@mthompson440 are you trying to simplify both sides of the equation?

Answer 3

I don't know..?

Answer 4

32^1/2= 16

Answer 5

Divide both sides by 16.

Answer 6

\[\large4^{2x}=32^{1/2}\]\[\large (2^2)^{2x} = (2^5)^{1/2}\]\[\large 2^{4x} = 2^{5/2}\]\[\large 4x = \frac{5}{2}\]\[\large x=~?\]

Answer 7

Ok.. But I don't understand how to solve it.

Answer 8

@Jhannybean explained it

Answer 9

Your goal is to make the same base so you can evaluate their powers.

Answer 10

X= 5/8?

Answer 11

incorrect

Answer 12

32 = 2 * 2 * 2 * 2 * 2

4 = 2 * 2

Theres an exponent rule that states having the same base allows for you to evaluate powers. \[\large a^x = a^y \implies x=y\]

Answer 13

Yes @calecea . That is correct.

Answer 14

@Jhannybean i thought it was 1

Answer 15

@mthompson440 I kind of get it. I mean it's half of 32, but it was just confusing it's it's the exponent, not like multiplication.

Answer 16

\[4x=\frac{5}{2} \implies x = \frac{5}{2\cdot 4} = \frac{5}{8} \ne 1\]

Answer 17

@jhannybean thank you!

Answer 18

@Jhannybean Oh lol

Answer 19

@mthompson440 32\(^{1/2}\) \(\ne\) 16

Answer 20

How do you get the 1/2 up there like that?

Answer 21

\[32^{1/2} =\sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{4^2 \cdot 2} = 4\sqrt{2} \ne 16\]

Answer 22

what do you mean, "up there like that?"

Answer 23

like by the 32

Answer 24

\[32^1/2\]

Answer 25

`^{1/2}`

Answer 26

nvm figured it out

Answer 27

Have you learned exponential functions, @calecea ?

Answer 28

example problem: \(\large 7^{5x+3} = 512\)

Answer 29

Now try solving this one.

Answer 30

I have no idea. Probably.

Answer 31

Using our knowledge of log rules, we know that: \(\log (a)^b \implies b\log(a)\)

Answer 32

Okay, let's try that one instead.

Answer 33

\[\large \log(x) +\log(x+48)=2\]

Answer 34

Let me know how far you've gotten with it.