Question

Expand log sqrt3x/4x^2-9 using the properties and rules for logarithms.

Answer 1

Given

`log\sqrt[]{(3x)/(4x^2-9)}`

Rewritten as

`\log ((3x)/(4x^2-9))^{(1)/(2)}`

Then, Apply properties of logarithms

`(1)/(2)\log ((3x)/(4x^2-9))`

The logarithm of a quotient is

`(1)/(2)\lbrack\log 3x-\log (4x^2-9)\rbrack`

And we expand each expression

`(1)/(2)\lbrack\log 3x-\log 4x^2+\log 9\rbrack`

Answer: B