## JayDS Group Title Find the equation of the inverse of the following. one year ago one year ago

1. JayDS Group Title

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

2. Jusaquikie Group Title

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 Group Title

yep, I did that.

4. Jusaquikie Group Title

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

5. JayDS Group Title

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

6. JayDS Group Title

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

7. Jusaquikie Group Title

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

8. Jusaquikie Group Title

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

9. Jusaquikie Group Title

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

10. JayDS Group Title

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

11. Jusaquikie Group Title

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 Group Title

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

13. JayDS Group Title

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

14. Jusaquikie Group Title

yeah i get confused too when you start using logs

15. Jusaquikie Group Title

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 Group Title

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

17. Jusaquikie Group Title

log 2 x or log 3 x?

18. Jusaquikie Group Title

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

19. JayDS Group Title

3x

20. JayDS Group Title

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

21. Jusaquikie Group Title

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

22. JayDS Group Title

after you switch the x and y I believe?

23. Jusaquikie Group Title

sorry i'm trying to remember this as we go

24. JayDS Group Title

it's ok.

25. Jusaquikie Group Title

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

26. JayDS Group Title

you wrote it wrong then.

27. Jusaquikie Group Title

all i did was change the exponent to a log

28. JayDS Group Title

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

29. JayDS Group Title

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

30. JayDS Group Title

then we can switch the x & y from there.

31. Jusaquikie Group Title

it's hard to do math on these boards lol

32. JayDS Group Title

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

33. JayDS Group Title

using the equation tab*

34. Jusaquikie Group Title

i think i have it let me check with my calculator

35. JayDS Group Title

kk.

36. Jusaquikie Group Title

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 Group Title

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

38. JayDS Group Title

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

39. Jusaquikie Group Title

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 Group Title

yes.

41. Jusaquikie Group Title

so let's try the second one

42. Jusaquikie Group Title

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

43. JayDS Group Title

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

44. JayDS Group Title

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

45. JayDS Group Title

thanks for the help.