Question

URGENT!!! 30 POINTS!!!Expand log(1/2)(3x^2/2) using properties and rules for logarithms.

Answer 1

$\log_\frac{1}{2}\left(\dfrac{3x^2}{2}\right)=\log_\frac{1}{2}3x^2-\log_\frac{1}{2}2=\log_\frac{1}{2}3+\log_\frac{1}{2}x^2-\log_\frac{1}{2}2\\\\=\log_\frac{1}{2}(3)+2\log_\frac{1}{2}(x)-\log_\frac{1}{2}\left(\dfrac{1}{2}\right)^{-1}\\\\=\log_\frac{1}{2}(3)+2\log_\frac{1}{2}(x)-\left[-\log_\frac{1}{2}\left(\dfrac{1}{2}\right)\right]\\\\=\log_\frac{1}{2}(3)+2\log_\frac{1}{2}(x)+\log_\frac{1}{2}\left(\dfrac{1}{2}\right)\\\\=\boxed{\log_\frac{1}{2}(3)+2\log_\frac{1}{2}(x)+1}$

$Used:\\\\\log_a\dfrac{b}{c}=\log_ab-\log_ac\\\\\log_a(bc)=\log_ab+\log_ac\\\\\log_ab^n=n\log_ab\\\\\log_aa=1$