Simplifying Logs

Question

Simplify: $$\frac{\log a + \log b - \log c}{\log d^2}$$

Using the basic properties of logs, the numerator should simplify to $\log (ab/c)$, if I'm not mistaken. The denominator $\log d^2 = 2 \log d$ but I don't know where to go from there. Can it be further simplified?

you can go any farther; answer is $\frac{\log(ab/c)}{2\log d}.$ — abel, May 14 '15 at 02:34
Eh. You could do change of base, but arguably that makes it worse. — jgon, May 14 '15 at 02:39
So the best answer here is probably just the simplification of the numerator as described above? — Lulu Uy, May 14 '15 at 02:43

score 1 · Answer 1 · answered May 14 '15 at 02:57

1

You may further simplify this to: $log_d \sqrt{\frac{ab}{c}}$ As Jgon suggested.

answered May 14 '15 at 02:57

Moti

1,928

How exactly does that work, I don't understand ? – Lulu Uy May 14 '15 at 02:59
$log{a}/log{b}=log_b{a}$ I leave it to you to prove. Good exercise for practice. – Moti May 14 '15 at 03:00
I understand this now, but how do you turn the d^2 into the square root of ab/c ? – Lulu Uy May 14 '15 at 03:11
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Don't square the d, use the 2 that you get from $logd^2 =2logd$ to divide the numerator.. – Moti May 14 '15 at 03:23

Simplifying Logs

1 Answers1