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

- anonymous

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

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- anonymous

32 to the power of 1/2

- anonymous

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

- anonymous

I don't know..?

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## More answers

- anonymous

32^1/2= 16

- anonymous

Divide both sides by 16.

- Jhannybean

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

- anonymous

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

- anonymous

@Jhannybean explained it

- Jhannybean

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

- anonymous

X= 5/8?

- anonymous

incorrect

- Jhannybean

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. \[\large a^x = a^y \implies x=y\]

- Jhannybean

Yes @calecea . That is correct.

- anonymous

@Jhannybean i thought it was 1

- anonymous

@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.

- Jhannybean

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

- anonymous

@jhannybean thank you!

- anonymous

@Jhannybean Oh lol

- anonymous

##### 1 Attachment

- Jhannybean

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

- anonymous

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

- Jhannybean

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

- anonymous

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

- anonymous

like by the 32

- anonymous

\[32^1/2\]

- Jhannybean

`^{1/2}`

- anonymous

nvm figured it out

- Jhannybean

Have you learned exponential functions, @calecea ?

- Jhannybean

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

- Jhannybean

Now try solving this one.

- anonymous

I have no idea. Probably.

- Jhannybean

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

- Jhannybean

Okay, let's try that one instead.

- Jhannybean

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

- Jhannybean

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

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