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

2. King Group Title

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

3. Tomas.A Group Title

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

4. slaaibak Group Title

Chuck norris can

5. King Group Title

oh sorry wait also given xy^2=4

6. King Group Title

$xy ^{2}=4$

7. King Group Title

now can u solve?

8. slaaibak Group Title

Yep

9. Tomas.A Group Title

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

10. King Group Title

11. slaaibak Group Title

$\log_3 (\log_2 x) - \log_3(-\log_2 y) = 1$ $\log_3({ \log_2 x \over -\log_2 y }) = 1$ $3 = { \log_2 x \over -\log_2 y }$ 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 Group Title

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

13. King Group Title

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

14. slaaibak Group Title

Yep

15. King Group Title

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

16. Tomas.A Group Title

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 Group Title

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

18. King Group Title

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

19. Tomas.A Group Title

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

20. Mertsj Group Title

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21. Mertsj Group Title

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 Group Title

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

23. King Group Title

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 Group Title

Sorry. Forgot about the 4. x = 64

25. slaaibak Group Title

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

26. King Group Title

i tried i didnt get it.....

27. slaaibak Group Title

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

28. Mertsj Group Title

Good luck to you, King

29. King Group Title

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 Group Title

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

31. Mertsj Group Title

yw and thanks

32. King Group Title

and thnx slaibaak u also helped me!!!!

33. King Group Title

why thanks?

34. Mertsj Group Title

You wished me good luck

35. King Group Title

oh ok !!bye now i gtg!!

36. Mertsj Group Title

Bye