Question

Which is 2logx-6log(x-9) written as a single logarithm

Answer 1

Answer: option c.

Step-by-step explanation:

 To solve the given exercise and write the expression as a single logarithm, you must keep on mind the following properties:

$m*log(a)=log(a)^m$

$log(a)-log(b)=log(\frac{a}{b})$

Therefore, by applying the properties shown above, you can rewrite the expression given, as following:

$2logx-6log(x-9)=logx^2-log(x-9)^6=log(\frac{x^2}{(x-9)^6})$

Then as you can see, the answer is the option c.