SOLUTION: I need help solving this problem {{{log (b, A)}}}=3 and {{{log (b, B)}}}= (-2). Find {{{log (b, cube root AB)}}}).

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I need help solving this problem {{{log (b, A)}}}=3 and {{{log (b, B)}}}= (-2). Find {{{log (b, cube root AB)}}}).      Log On


   

Question 693738: I need help solving this problem
log+%28b%2C+A%29=3 and log+%28b%2C+B%29= (-2). Find log+%28b%2C+cube+root+AB%29).
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
log (b, A)}}}=3 and log+%28b%2C+B%29= (-2).
Find log+%28b%2C+cube+root+AB%29).
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logb(A) = 3
logb(B) = -2
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Then logb(AB)^(1/3) = (1/3)[logb(A)+logb(B)
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= (1/3)logb(A) + (1/3)logb(B)
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= (1/3)3 + (1/3)(-2)
----
= 1 - 2/3
====
= 1/3
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cheers,
Stan H.
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