SOLUTION: I can't seem to get this.. no matter what I do Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent po

Question 466402: I can't seem to get this.. no matter what I do
Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive numbers.

9 log w + 4 log z - log (x - 5)

A) log w^4*z^9/(x-5)
B) log (x-5)/w^9*z^4
C) log w^9*z^4/x-5
D) log w^9*(x-5)/z^4

Any help would be appreciated
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
here's how it works:
your equation is:
9 log w + 4 log z - log (x - 5)
you have 3 basic concepts working here:
concept number 1:
log (a^b) = b*log(a)
concept number 2:
log (a * b) = log(a) + log(b)
concept number 3:
log (a / b) = log(a) - log(b)
using these concept your equation will be transformed as follows:
9 log w + 4 log z - log (x - 5)
using concept 1, you get:
log(w^9) + log(z^4) - log(x - 5)
working from left to right:
using concept 2, you get:
log(w^9 * z^4) - log(x - 5)
using concept 3, you get:
log( (w^9 * z^4) / (x - 5) )
This looks a lot like it matches selection C) log w^9*z^4/x-5

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