Question

Which expression is equivalent to log c x2-1/5x

Answer 1

Hello! For this problem we need to make use of two existing logarithmic properties. These are:

1.
`log (M)/(N)` is equal to
`log M-logN`
2.
`log(MN)` is equal to
`log M+logN`

Following the first property, we can simplify the expression to
`log (x^(2)-1)-log(5x)`.

Then, we will use the second property to the term 5x. The final form of the expression would then be
`log(x^(2)-1)-(log5+logx)`.

ANSWER:
`log(x^(2)-1)-(log5+logx)` (third option)

Answer 2

Answer
C is the correct answer

㏒(x²-1) - (㏒5 + ㏒x)


Step-by-step explanation
The law of logarithm says;
㏒AB = ㏒₃A + ㏒₃B
㏒C/B = ㏒₃C - ㏒₃B
So, the given equation will be,

㏒((x²-1)/5x) = ㏒(x²-1) - ㏒5x
= ㏒(x²-1) - (㏒5 + ㏒x)