SOLUTION: If logx/a=logy/2=logz/5=k and x^4y^3z^-2=1 ,find a.

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Question 1046159: If logx/a=logy/2=logz/5=k and x^4y^3z^-2=1 ,find a.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
logx%2Fa=logy%2F2=logz%2F5 <===> log%28x%5E%281%2Fa%29%29=log%28y%5E%281%2F2%29%29=log%28z%5E%281%2F5%29%29 <===> x%5E%281%2Fa%29=y%5E%281%2F2%29=z%5E%281%2F5%29
===> x%5E2+=+y%5Ea, y%5E5+=+z%5E2, and x%5E5+=+z%5Ea.
The first equation implies that x%5E4+=+y%5E%282a%29.
From the given, x%5E4%2Ay%5E3%2Az%5E%28-2%29=1, or x%5E4%2Ay%5E3+=+z%5E2,
===> y%5E%282a%29%2Ay%5E3+=+y%5E5, after direct substitution.
===> y%5E%282a%2B3%29+=+y%5E5, or, highlight%28a+=+1%29.
N.B.: The value of k in the statement of the problem is irrelevant in getting the value of a.