Question

Which expression is equivalent to

Answer 1

Explanation:

`\log_(12)\left(((1)/(2))/(8w)\right)=\log_(12)\left((1)/(16w)\right)\qquad\text{use}\ a^(-1)=(1)/(a)\\\\=\log_(12)(16w)^(-1)\qquad\text{use}\ \log_ab^n=n\log_ab\\\\=-1\log_(12)(16w)\qquad\text{use}\ \log_a(bc)=\log_ab+\log_ac\\\\=-\left(\log_(12)16+\log_(12)w\right)=-\log_(12)2^4-\log_(12)w\qquad\text{use}\ \log_ab^n=n\log_ab\\\\=-4\log_(12)2-\log_(12)w`