SOLUTION: Please help me solve this question If m and n are positive real numbers such that 3 log m base 4 = 4 log n base 8 find: (I) a relation between m and n which does not involve loga

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help me solve this question If m and n are positive real numbers such that 3 log m base 4 = 4 log n base 8 find: (I) a relation between m and n which does not involve loga      Log On


   

Question 1184305: Please help me solve this question
If m and n are positive real numbers such that 3 log m base 4 = 4 log n base 8 find:
(I) a relation between m and n which does not involve logarithms
(II) the value of n if m=16 (leave your answer as a surf in the simplest form)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
3log%284%2Cm%29+=+4log%288%2Cn%29

===>log%284%2Cm%5E3%29+=+log%288%2Cn%5E4%29 <===> log%282%2Cm%5E3%29%2Flog%282%2C4%29+=+log%282%2Cn%5E4%29%2Flog%282%2C8%29 <===> log%282%2Cm%5E3%29%2F2+=+log%282%2Cn%5E4%29%2F3 <===> 3log%282%2Cm%5E3%29+=+2log%282%2Cn%5E4%29

===> log%282%2Cm%5E9%29+=+log%282%2Cn%5E8%29 ===> m%5E9+=+n%5E8.

If m = 16, then 16%5E9+=+n%5E8 ===> n+=+16%5E%289%2F8%29 ===> n+=+16sqrt%282%29.

***By the way, it is NOT a "surf" but a SURD.