Help Evaluating Logarithm
1. The problem statement, all variables and given/known data
Evaluate without a calculator: (log_{3}4 + log_{2}9)^{2}  (log_{3}4  log_{2}9)^{2} 2. Relevant equations 3. The attempt at a solution (log_{3}4 + log_{2}9)^{2}  (log_{3}4  log_{2}9)^{2} (2log_{3}2 + 2log_{2}3)^{2}  (2log_{3}2  2log_{2}3)^{2} And now I'm stuck.... 
Re: Help Evaluating Logarithm
Quote:
Try using this fact a^{2}b^{2} = (a+b)(ab). 
Re: Help Evaluating Logarithm
[tex]a^2b^2=(ab)(a+b)[/tex]
EDIT: how to delete message 
Re: Help Evaluating Logarithm
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(log_{3}4 + log_{2}9)^{2} to (log_{3}4^{2} + log_{2}9^{2}), which is not true. 
Re: Help Evaluating Logarithm
Ohhhhh, I see. I shall reattempt now. Thanks.

Re: Help Evaluating Logarithm
Hmmm. I think it's simpler than that, guys 
Setting A = log_{3}4 and B = log_{2}9 (A+B)^{2}  (AB)^{2} = (A^{2} + 2AB + B^{2})  (A^{2}  2AB + B^{2}) ... and later on using that log_{n}x^{k} = k.log_{n}x and that log_{a}b [itex]\times[/itex] log_{b}c = log_{a}c 
Re: Help Evaluating Logarithm
Erm...Nevermind. I'm still stuck. Can someone walk me through it please?
Edit: I totally forgot about factoring. I'll try that, thanks!! 
Re: Help Evaluating Logarithm
try this (A+B)^2  (AB)^2 = X^2  Y^2 = ( X + Y ) ( X  Y )
where X=(A+B) and Y=(AB) and you get (A+B)^2  (AB)^2 =(2A) (2B) = 4AB 
Re: Help Evaluating Logarithm
Okay one of my friends just told me to try changing the base. I did that, and now I have a giant mess on my hands. I have
(ln2*ln4 + ln3*ln9 / ln3*ln2)^2  (ln2*ln4  ln3*ln9 / ln3*ln2)^2 and somehow I'm supposed to get 16 from all of that. I'm not really sure how... 
Re: Help Evaluating Logarithm
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Re: Help Evaluating Logarithm
Okie. Trying again now.
Edit: I just can't seem to do it no matter what I try :( 
Re: Help Evaluating Logarithm
Show us what you have so far.

Re: Help Evaluating Logarithm
Well I tried applying this:
Setting A = log34 and B = log29 (A+B)2  (AB)2 = (A2 + 2AB + B2)  (A2  2AB + B2) The A2's and B2's will cancel out leaving me with 4AB which would be 4(log_{3}4 * log_{2}9) The answer in the book says I'm supposed to get 16. I tried changing the base to get 4(ln4*ln9 / ln3*ln2) I think I could maybe do 4(2ln2*2ln3 / ln3*ln2) but I'm not sure if that's correct. I think then maybe the ln2's and ln3's would cancel out leaving me with 4(2*2) which would be 16. But I'm not sure if that's correct. 
Re: Help Evaluating Logarithm
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Re: Help Evaluating Logarithm
Yay!!! Thanks so much everyone!

Re: Help Evaluating Logarithm
Also, if you didn't want to change base,
[tex] \begin{align} log_34 \times log_29 & = log_32^2 \times log_23^2\\ &= 2log_32 \times 2log_23\\ &= 4(log_32.log_23)\\ &= 4(log_33) \\ &=4 \end{align} [/tex] 
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