SOLUTION: Hello, I have a problem that asks the following: find {{{ log(a, (x^2) (z^3)/ (sqrt (y))) }}} where {{{ log(a,x)}}}=2, {{{log(a, y)}}}=6, and {{{log(a,z)}}}=-2 I know th

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello, I have a problem that asks the following: find {{{ log(a, (x^2) (z^3)/ (sqrt (y))) }}} where {{{ log(a,x)}}}=2, {{{log(a, y)}}}=6, and {{{log(a,z)}}}=-2 I know th      Log On


   

Question 461926: Hello,
I have a problem that asks the following:
find +log%28a%2C+%28x%5E2%29+%28z%5E3%29%2F+%28sqrt+%28y%29%29%29+
where +log%28a%2Cx%29=2, log%28a%2C+y%29=6, and log%28a%2Cz%29=-2
I know the answer is -5; how to get there is beyond me. A little help would be amazing!
Thanks,
Jessica
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find loga[(x^2) (z^3)/ (sqrt (y)))
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= loga(x^2) + loga(z^3) - loga(sqrt(y))
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= 2loga(x) + 3loga(z) - (1/2)loga(y)
---

where loga(x)=2, loga(y)=6, and loga(z)=-2
----
substitute to get:
---
= 2*2 + 3(-2) - (1/2)6
---
= 4 - 6 - 3
---
= -5
===========================
Cheers,
Stan H.
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