Question

Marcus is proving the Product Rule of Logarithms. The following is his work so far.

Let logbm=x
and logbn=y
.

logbm=x
is equivalent to bx=m
.

logbn=y
is equivalent to by=n
.

Therefore, mn=bxby
.



Which of the following options best describes the next step Marcus should take in his proof?

Option #1: Use the Product Rule of Exponents to rewrite the equation as mn=bx+y
.

Option #2: Rewrite this exponential equation as a logarithmic equation.

Option #3: Substitute specific values for m, n, x, and y.

(1 point)
The option that best describes the next step in the proof is Option #

Answer 1

The best option for the next step in Marcus's proof is **Option #1**: Use the Product Rule of Exponents to rewrite the equation as \( mn = b^{x+y} \).

This follows logically because \( b^{x} \cdot b^{y} = b^{x+y} \) is the Product Rule of Exponents. Therefore, it’s the correct way to proceed from \( mn = b^{x} \cdot b^{y} \). The next logical step would be to relate this back to logarithms.