3logx-logy-5logz
(logx cubed/log y)/logz to the fifth power??
Here’s an easy way to check your answer: simply pick some values for x, y, and z – say 2, 3, and 5. Plug these into the original form and note the answer. Next, plug them into your condensed form to see if you get the same answer.
If you perform this test, you’ll find that your answer is not correct. This suggests we should re-examine the “log rule” we are trying to apply.
If we were expanding the expression log(ab), we’d write
log(ab) = log(a) + log(b)
If we’re condensing, then
log(a) + log(b) = log(ab)
Similarly,
log(a) - log(b) = log(a/b)… NOT log(a)/log(b)!
With these tips in mind, give your problem another try.
