## King 3 years ago $\log_{3} (\log_{2} x) + \log_{1/3} (\log_{1/2} y)]=1 • This Question is Closed 1. Tomas.A \[\log_{3} (\log_{2} x) + \log_{1/3} (\log_{1/2} y)=1$

2. King

ya ure rite !!!!!!!now pls solve!

3. Tomas.A

you can't solve because you have two variables and one equation

4. slaaibak

Chuck norris can

5. King

oh sorry wait also given xy^2=4

6. King

$xy ^{2}=4$

7. King

now can u solve?

8. slaaibak

Yep

9. Tomas.A

$\begin{cases}\log_{3} (\log_{2} x) + \log_{1/3} (\log_{1/2} y)=1\\xy ^{2}=4\end{cases}$

10. King

11. slaaibak

$\log_3 (\log_2 x) - \log_3(-\log_2 y) = 1$ $\log_3({ \log_2 x \over -\log_2 y }) = 1$ $3 = { \log_2 x \over -\log_2 y }$ x=y^2/4 $3 ={{ {\log_2{ y^2\over4}} } \over -\log_2 y}$ I'm not sure if I did everything correctly, but you can try to solve it further. If I made no mistakes, it's not too hard from here

12. slaaibak

Oops, there I see my mistake. x= 4/y^2 So just fix the last substitution

13. King

ummm.can u wait i shall try and get the answer and can u check if it is rite?

14. slaaibak

Yep

15. King

ummm...how do u get the answer??:(::(:(:(

16. Tomas.A

sorry but solving those logarithms is just waste of time, it's only technical thing, so you'd better show how you solve and then i can say what's wrong

17. King

but the thing is i dont know how to go on furtheer.......

18. King

ok guys i got this $2-\log_{2} y ^{2}/\log_{2} y$

19. Tomas.A

$\log_nm^p=p\cdot\log_nm$ use this and stop spamming

20. Mertsj

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21. Mertsj

So y^-3 = x but x = 4/y^2 So y^-3 = 4/y^2 and y^-1 = 4 so y = 1/4 and x = 16

22. slaaibak

well, if you don't try, I won't show you how to do it. answer is x=64 y=1/4

23. King

thnx a lot mertsj..... and slaibaak look my sir taught us only basics and u think i am a fool i would rather do it on my own but i tried i didn't get it so i asked u guys if u didn't wanna help u could have said no ok...........

24. Mertsj

Sorry. Forgot about the 4. x = 64

25. slaaibak

Those were the basics. I practically gave you the answer, you just had to substitute and simplify

26. King

i tried i didnt get it.....

27. slaaibak

I don't think you are a fool, I only think you didn't try hard enough

28. Mertsj

Good luck to you, King

29. King

first of all i hate it that i had to ask fr hep i always try as hard as i can then ask fr help......so if u think i dont try hard enough well den thats ure opinion...so frgt it.........

30. King

thnx again mertsj Good luck to u 2!!!!!

31. Mertsj

yw and thanks

32. King

and thnx slaibaak u also helped me!!!!

33. King

why thanks?

34. Mertsj

You wished me good luck

35. King

oh ok !!bye now i gtg!!

36. Mertsj

Bye