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 #
.
Remaining Attempts : 3
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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 #
.
Remaining Attempts : 3
Skip to navigation
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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=bx+y.**
This is because, given the equation \(mn = b^x b^y\), Marcus can apply the Product Rule of Exponents (which states that \(a^m \cdot a^n = a^{m+n}\)) to combine the exponents on the base \(b\). This leads to \(mn = b^{x+y}\), which is crucial for demonstrating the desired logarithmic relationship.
**Option #1: Use the Product Rule of Exponents to rewrite the equation as mn=bx+y.**
This is because, given the equation \(mn = b^x b^y\), Marcus can apply the Product Rule of Exponents (which states that \(a^m \cdot a^n = a^{m+n}\)) to combine the exponents on the base \(b\). This leads to \(mn = b^{x+y}\), which is crucial for demonstrating the desired logarithmic relationship.
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