# Math Help - contract this log

1. ## contract this log

Hey guys how do you contract this log? -4log√y + 3/2log9x⁴+ ½log3√z

2. $-4 log\sqrt{y} + \frac32 log(9x^4) + \frac12 log(3\sqrt{z})$

Hm... use this rule:

$a\ log (x) = log(x^a)$

$log\sqrt{y^{-4}} + log(9x^4)^\frac32 + log(3\sqrt{z})^\frac12$

Rewrite all the powers

$log((y^{\frac12})^-4) + log(9x^4)^{\frac32} + log(3z^\frac12)^{\frac12}$

Simplify;

$log(y^{-2}) + log(3x^2)^3 + log(3^{\frac12}z^\frac14)$

$log(\frac{1}{y^2}) + log(27x^6) + log(3^{\frac12}z^\frac14)$

Now, combine the terms since they have a common base.

$log((\frac{1}{y^2})(27x^6)(3^{\frac12}z^\frac14))$

Simplify...

$log (\frac{27 \sqrt{3}x^6 z^{\frac14} }{y^2})$