# Simplifying Logs

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 2:34
• Eh. You could do change of base, but arguably that makes it worse. – jgon May 14 '15 at 2:39
• So the best answer here is probably just the simplification of the numerator as described above? – Lulu Uy May 14 '15 at 2:43

You may further simplify this to: $log_d \sqrt{\frac{ab}{c}}$ As Jgon suggested.
• $log{a}/log{b}=log_b{a}$ I leave it to you to prove. Good exercise for practice. – Moti May 14 '15 at 3:00
• Don't square the d, use the 2 that you get from $logd^2 =2logd$ to divide the numerator.. – Moti May 14 '15 at 3:23