## 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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1. anonymous

32 to the power of 1/2

2. anonymous

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

3. anonymous

I don't know..?

4. anonymous

32^1/2= 16

5. anonymous

Divide both sides by 16.

6. anonymous

$\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=~?$

7. anonymous

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

8. anonymous

@Jhannybean explained it

9. anonymous

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

10. anonymous

X= 5/8?

11. anonymous

incorrect

12. anonymous

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. $\large a^x = a^y \implies x=y$

13. anonymous

Yes @calecea . That is correct.

14. anonymous

@Jhannybean i thought it was 1

15. 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.

16. anonymous

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

17. anonymous

@jhannybean thank you!

18. anonymous

@Jhannybean Oh lol

19. anonymous

20. anonymous

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

21. anonymous

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

22. anonymous

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

23. anonymous

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

24. anonymous

like by the 32

25. anonymous

$32^1/2$

26. anonymous

^{1/2}

27. anonymous

nvm figured it out

28. anonymous

Have you learned exponential functions, @calecea ?

29. anonymous

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

30. anonymous

Now try solving this one.

31. anonymous

I have no idea. Probably.

32. anonymous

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

33. anonymous

Okay, let's try that one instead.

34. anonymous

$\large \log(x) +\log(x+48)=2$

35. anonymous

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