Question

What is log(21/x2) written in expanded form?

log 21−2 log x

2 log x−log 21

2 log 21−log x

log x−log 21+2

Answer 1

`log(21)-2log(x)`

Explanation:

The given logarithmic expression is
`log((21)/(x^2) )`.

Observe that the expression in the argument is a quotient.

We apply the quotient property. This property is given as follows:

`log((A)/(B))=log(A)-log(B)`.

When we apply this property, we obtain,

`log((21)/(x^2))=log(21)-log(x^2)`.

Recall that
`log_a(m^n)=n\:log_a(m)`.

We now apply this property to obtain,

`log((21)/(x^2))=log(21)-2log(x)`.

Therefore the correct answer is A