Question

Condense the expression to the logarithm of a single quantity.

I'm going to be so thankful if anyone could solve this for me please... because I can't understand any of it right now.​

Answer 1

`\frac 12 \log_3 x - 2\log_3 (y +8)\\ \\=\log_3 x^(\tfrac 12)- \log_3(y+8)^2~~~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]\\\\=\log_3 \left( \frac {x^(\tfrac 12)}{y+8)^2} \right)~~~~~~~~~~~~~~~~~~~~~~~~;\left[\log_b \left( \frac mn \right) = \log_b m - \log_b n \right]`