Question

Rewrite the following expression as a single logarithm 2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)

Answer 1

The rewritten form of the expression as a single logarithm is; log {(x+3)²(x-2)^5}/(x-7)³(x²).

What is the rewritten form of the expression?

The expression given in the task content can be rewritten as a single logarithm by virtue of the laws of logarithms as follows;

2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)

= log(x+3)² - log(x-7)³ +log(x-2)^5-log(x^2)

= log {(x+3)²(x-2)^5}/(x-7)³(x²)

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