# Math Help - LOGS

1. ## LOGS

If log a = 2 and log b = 3, what is the numerical value of [log sqrt{a}/log (b^3)]?

2. Originally Posted by magentarita
If log a = 2 and log b = 3, what is the numerical value of [log sqrt{a}/log (b^3)]?
Use this propery :
$\log a^b=b \log(a)$

hence :
$\frac{\log \sqrt{a}}{\log b^3}=\frac{\log a^{1/2}}{\log b^3}=\frac{\frac 12 ~ \log(a)}{3 \log(b)}$

I'm sure you can finish :P

3. ## yes..........

Originally Posted by Moo
Use this propery :
$\log a^b=b \log(a)$

hence :
$\frac{\log \sqrt{a}}{\log b^3}=\frac{\log a^{1/2}}{\log b^3}=\frac{\frac 12 ~ \log(a)}{3 \log(b)}$

I'm sure you can finish :P
Yes, I can finish.

Thanks