How to do this two A Math logarithm questions?

AmuletxHeart SG

Express Y in terms of X.

Forbiddensinner SG

Express Y in terms of X.

This single statement is not going to allow us to help you .....

You will need to give more information.

Anyway....Shugo Chara?

LatecomerX SG

Express Y in terms of X.

X X
X X
  X
  X
  X

SBS261P SG

X X
X X
  X
  X
  X

LOL =D

AmuletxHeart SG

Opps how to edit my original post? The scanned picture ain't showing up.

AmuletxHeart SG

Anyways heres the questions:

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ThunderFbolt SG

these are actually rather standard questions. the thing to remember is that

log_x (x) = 1 (meaning the log in base x working on x is 1)

a log b = log b^a (meaning b to the power of a, like 3 to the power of 2 is 9)

log x + log y = log xy

AmuletxHeart SG

Arg I hate the time limit between posts imposed on newbs.

Anyway, here is where I'm stuck at question C.

2 log_3 (y) - 4 = 3 log_3(x+2)

log_3 y^2 - 4log _3 (3) = log_3 (x+2)^3

log_3 y^2 - log_3(3^4) = log_3 (x+2)^3

So how to remove the logs and make it just X and Y?

Thanks.

Forbiddensinner SG

Arg I hate the time limit between posts imposed on newbs.

Anyway, here is where I'm stuck at question C.

2 log_3 (y) - 4 = 3 log_3(x+2)

log_3 y^2 - 4log _3 (3) = log_3 (x+2)^3

log_3 y^2 - log_3(3^4) = log_3 (x+2)^3

So how to remove the logs and make it just X and Y?

Thanks.

Remember that log a + log b = log ab and log a - log b = log a/b

Hence, log(3) y^2 - log(3) 3^4 is the same as log (3) y^2/ 81

Thus, log(3) y^2/ 81 = log(3) (x + 2)^3, and y^2/ 81 = (x + 2)^3

y^2 = 81(x + 2)^3

y = sqrt(81(x + 2)^3)

y= 9sqrt(x + 2)^3 or y= -9sqrt(x + 2)^3

Amu-chan.

ThunderFbolt SG

From log x + log y = log xy

Your working would continue to become

log_3 ((y^2)/(3^4)) = log_3 ((x+2)^3)

Which would allow you to remove logs from both sides to get

(y^2)/(3^4) = (x+2)^3

Where you can easily find y.

Remember that you can only remove them like this when both logs are in the same base and there is only 1 log term on each side.

And since y is squared, you may need your ± sign.

Edit: Beaten by 4 mins, ah well. =)

Forbiddensinner SG

From log x + log y = log xy

Your working would continue to become

log_3 ((y^2)/(3^4)) = log_3 ((x+2)^3)

Which would allow you to remove logs from both sides to get

(y^2)/(3^4) = (x+2)^3

Where you can easily find y.

Remember that you can only remove them like this when both logs are in the same base and there is only 1 log term on each side.

And since y is squared, you may need your ± sign.

Edit: Beaten by 4 mins, ah well. =)

Nvm, it is the heart that matters.

Besides, this serves as double confirmation.

Rooney9 SG

Nvm, it is the heart that matters.

Besides, this serves as double confirmation.

u r a math genius. btw double confirmation is redundant, just like repeat again.

or reverse backwards.

SBS261P SG

u r a math genius. btw double confirmation is redundant, just like repeat again.

or reverse backwards.

ppl math pro only mah. haha just kidding.

sometimes if you reuse the terms again and again (ahem this is also redundant) it might just stick! like "brokeback" which apparently has been included in the dictionary (",)