Question

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers.

log4 7 -log4 m

Options:
1) log4 (m / 7)
2) log8 (7 / m)
3) log4 (7 / m)
4) log4 (7 - m)

Answer 1

Option 3:
`log_(4) ((7)/(m) )`

Explanation:

Logarithmic functions represented by
`log_(b) x = y` means that
`x = b^(y)` where x > 0, b > 0, and b ≠ 1.

According to the quotient rule:

`log_(b) ( (M)/(N) ) = log_(b)M - log_(b)N`

In the given problem, since both logs have the same base = 4, then we can model
`log_(4) 7 - log_(4) m` to the quotient rule, resulting in:

Quotient rule:
`log_(b) ( (M)/(N) ) = log_(b)M - log_(b)N`

`log_(4)7 - log_(4)m = log_(4) ( (7)/(m) )`

Therefore, the correct answer is Option 3:
`log_(4) ((7)/(m) )`