## JayDS 3 years ago Find the equation of the inverse of the following.

1. JayDS

$y=3^{x}$ $y=_{5}x$

2. Jusaquikie

the inverse is just if you put in an x and get a y the inverse is like putting in the y and getting the same x you put in the first part.

3. JayDS

yep, I did that.

4. Jusaquikie

what you can do is switch your x's and y's then just solve for y.

5. JayDS

$y=3^{x}$ $x=3^{y}$ $\log _{10}x = \log _{10}3^{y}$ $\log _{10} x = ylog _{10}3$ $y=\frac{\log _{10}x}{\log _{10}3}$ y=x/3?

6. JayDS

I have answers but I want to know what I did wrong, because it seems right to me.

7. Jusaquikie

i think you need to keep the logs or put e^y

8. Jusaquikie

you can only take away the logs like you did if y had one on that side

9. Jusaquikie

i think it can be rewrote as y=ln(x-3) but i'm a little rusty with logarithms

10. JayDS

but there is log10 on both sides, so I can cancel it out? and ok... I'm still confused sorry.

11. Jusaquikie

when you moved the y over to the other sice you had y=log(x)/log(3) y doesn't have a log

12. Jusaquikie

if it was log(y)=log(x)/log(3) you could cancel them out

13. JayDS

really? hmmm, confusing but I know what you mean.

14. Jusaquikie

yeah i get confused too when you start using logs

15. Jusaquikie

if you have the answer try to work it backwards to get the first question and try to tie the two to gether with what your sure of.

16. JayDS

the answer is $\log _{3}x for x>0$ can you help me out? I don't understand how they got it.

17. Jusaquikie

log 2 x or log 3 x?

18. Jusaquikie

$\log_{a}y=x$ is $a^{x}=y$

19. JayDS

3x

20. JayDS

from log10(x)=ylog10(3) can you show me the rest of the steps?

21. Jusaquikie

so we can rewriteyour first one as as$\log_{3} x=y$

22. JayDS

after you switch the x and y I believe?

23. Jusaquikie

sorry i'm trying to remember this as we go

24. JayDS

it's ok.

25. Jusaquikie

no that is just rewriting it then we swith and solve for x

26. JayDS

you wrote it wrong then.

27. Jusaquikie

all i did was change the exponent to a log

28. JayDS

$y=3^{x}$ $\log _{3}y=x$

29. JayDS

I think you got confused with the x and y, you just got them in the wrong position.

30. JayDS

then we can switch the x & y from there.

31. Jusaquikie

it's hard to do math on these boards lol

32. JayDS

yeh I know haha, especially trying to write the equation takes years.

33. JayDS

using the equation tab*

34. Jusaquikie

i think i have it let me check with my calculator

35. JayDS

kk.

36. Jusaquikie

ok lol i can't figure out how to do it on my calculator but i think it's right, so all we are doing is changing the question into a log of the same equasion then when we swap x and y we already have the answer

37. Jusaquikie

by the rules of logarithms we have loga^b=c is the same as a^c=b

38. JayDS

ok, and it turns out to be$y=\log _{3}x$ right?

39. Jusaquikie

so taking your problem y=3^x and putting it in log form we get log3^y=x then we swap y and x to get log3^x=y is that right?

40. JayDS

yes.

41. Jusaquikie

so let's try the second one

42. Jusaquikie

y=5^x is log5^y=x so swap is log5^x=y

43. JayDS

yep but the answer only says 5^x for some reason.

44. JayDS

confusing, I'll just have to ask my teacher. I'm just doing it advanced anyway.

45. JayDS

thanks for the help.

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