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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.032 to the power of 1/2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@mthompson440 are you trying to simplify both sides of the equation?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Divide both sides by 16.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\large4^{2x}=32^{1/2}\]\[\large (2^2)^{2x} = (2^5)^{1/2}\]\[\large 2^{4x} = 2^{5/2}\]\[\large 4x = \frac{5}{2}\]\[\large x=~?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok.. But I don't understand how to solve it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Jhannybean explained it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Your goal is to make the same base so you can evaluate their powers.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.032 = 2 * 2 * 2 * 2 * 2 4 = 2 * 2 Theres an exponent rule that states having the same base allows for you to evaluate powers. \[\large a^x = a^y \implies x=y\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes @calecea . That is correct.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Jhannybean i thought it was 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[4x=\frac{5}{2} \implies x = \frac{5}{2\cdot 4} = \frac{5}{8} \ne 1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@jhannybean thank you!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@mthompson440 32\(^{1/2}\) \(\ne\) 16

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How do you get the 1/2 up there like that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[32^{1/2} =\sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{4^2 \cdot 2} = 4\sqrt{2} \ne 16\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what do you mean, "up there like that?"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Have you learned exponential functions, @calecea ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0example problem: \(\large 7^{5x+3} = 512\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now try solving this one.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have no idea. Probably.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Using our knowledge of log rules, we know that: \(\log (a)^b \implies b\log(a)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, let's try that one instead.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\large \log(x) +\log(x+48)=2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Let me know how far you've gotten with it.
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