Question

Rewrite the expression 16/8log(x+5)+16/4log(x^2+3)-4/8log(x+2) as a single logarithm

Answer 1

$$\dfrac{16}{8}\log(x+5)+\dfrac{16}{4}\log(x^2+3)-\dfrac{4}{8}\log(x+2)$$

$$=2\log(x+5)+4\log(x^2+3)-\dfrac{1}{2}\log(x+2)$$

$$=\log\dfrac{(x+5)^2(x^2+3)^4}{\sqrt{x+2}}$$