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## heathernelly 2 years ago ;)))

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1. jim_thompson5910

Similar Problem: $\Large \log_{3}(60) - \log_{3}(12)$ $\Large \log_{3}\left(\frac{60}{12}\right)$ $\Large \log_{3}(5)$ So $\Large \log_{3}(60) - \log_{3}(12) = \log_{3}(5)$

2. heathernelly

that's all i have to do?

3. jim_thompson5910

pretty much, but just use your numbers in place of mine

4. heathernelly

yeah, thanks! do you know how to do the other one?

5. jim_thompson5910

in general $\Large \log_{b}(x) - \log_{b}(y) = \log_{b}\left(\frac{x}{y}\right)$

6. jim_thompson5910

what do 16 and 64 have in common

7. heathernelly

they both have a 6 in them, both even #'s

8. jim_thompson5910

good, but in terms of factors

9. heathernelly

2^6? i don't know :S :/

10. jim_thompson5910

both are powers of 2 or powers of 4

11. heathernelly

ahh, yeah

12. jim_thompson5910

so 16 = 2^4 64 = 2^6 and 16 = 4^1 64 = 4^3

13. heathernelly

that's it?

14. jim_thompson5910

well you need to rewrite both sides to have the same base

15. jim_thompson5910

for instance, say you had 2^x = 16 you would rewrite 16 as 2^4 to get 2^x = 2^4 and you can see that x must be 4 (since both bases are 2)

16. jim_thompson5910

so you're using this idea to solve the second problem

17. heathernelly

ohhh, well that's pretty simple! thank youu

18. heathernelly

actually waait, it's not! haha.. i just got confused

19. jim_thompson5910

with what

20. jim_thompson5910

where are you stuck

21. heathernelly

and you can see that x must be 4 (since both bases are 2) ??

22. jim_thompson5910

well if b^x = b^y, then x = y

23. heathernelly

i'm confused because you did 2 different problems..:/

24. jim_thompson5910

that's just an example

25. heathernelly

okay, that makes sense .. but i'm still confused on what to do after what you said ''16 = 2^4 64 = 2^6 and 16 = 4^1 64 = 4^3''

26. jim_thompson5910

oh i meant to say 16 = 4^2, my bad

27. jim_thompson5910

1/16=64^(4x-3) 1/(4^2) = (4^3)^(4x-3) ... since 16 = 4^2 and 64 = 4^3 4^(-2) = 4^(3*(4x-3)) so because the bases are now the same, we can say that the exponents must be the same so... -2 = 3*(4x-3) solve for x

28. heathernelly

ahh, got it :) thanks a lot!!!

29. jim_thompson5910

np

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