You are proving the Quotient Rule of Logarithms. The following shows your work so far.

Question

Let logbm=x
and logbn=y
.

logbm=x
is equivalent to bx=m
.

logbn=y
is equivalent to by=n
.

Which of the following options best describes the next step you should take in this proof?

(1 point)
Responses

Write the product of m and n as mn=b^xb^y
.
Write the product of m and n as m n equals b superscript x baseline b superscript y baseline .

Write the difference between m and n as m−n=b^x−b^y
.
Write the difference between m and n as m minus n equals b superscript x baseline minus b superscript y baseline .

Write the sum of m and n as m+n=b^x+b^y
.
Write the sum of m and n as m plus n equals b superscript x baseline plus b superscript y baseline .

Write the quotient of m and n as m/n=b^x/b^y
.

Answer 1

In order to prove the Quotient Rule of Logarithms, the most relevant next step would be to express the relationship between \( m \) and \( n \). Since you are interested in the quotient \(\frac{m}{n}\) (which is the basis of the Quotient Rule), the appropriate next step would be:

Write the quotient of m and n as \( \frac{m}{n} = \frac{b^x}{b^y} \).

This step will allow you to apply the properties of exponents to show the relationship that leads to the final form of the quotient rule for logarithms, which states that \(\log_b(m/n) = \log_b(m) - \log_b(n)\).