Which option best describes how to show that the Product Rule of Logarithms works for the base 4 expression log416+log44 ?(1 point)ResponsesEvaluate both log416 and log44 and show that their sum is equal to the value of log464.Evaluate both logarithm subscript 4 baseline 16 and logarithm subscript 4 baseline 4 and show that their sum is equal to the value of logarithm subscript 4 baseline 64 .Evaluate both log416 and log44 and show that their sum is equal to the value of log420.Evaluate both logarithm subscript 4 baseline 16 and logarithm subscript 4 baseline 4 and show that their sum is equal to the value of logarithm subscript 4 baseline 20 .Evaluate both log416 and log44 and show that their product is equal to the value of log464.Evaluate both logarithm subscript 4 baseline 16 and logarithm subscript 4 baseline 4 and show that their product is equal to the value of logarithm subscript 4 baseline 64 .Evaluate both log416 and log44 and show that their product is equal to the value of log420.Evaluate both logarithm subscript 4 baseline 16 and logarithm subscript 4 baseline 4 and show that their product is equal to the value of logarithm subscript 4 baseline 20 .

Question

Which option best describes how to show that the Product Rule of Logarithms works for the base 4 expression  log416+log44 ?(1 point)ResponsesEvaluate both log416 and log44 and show that their sum is equal to the value of log464.Evaluate both  logarithm subscript 4 baseline 16  and  logarithm subscript 4 baseline 4  and show that their sum is equal to the value of  logarithm subscript 4 baseline 64 .Evaluate both log416 and log44 and show that their sum is equal to the value of log420.Evaluate both  logarithm subscript 4 baseline 16  and  logarithm subscript 4 baseline 4  and show that their sum is equal to the value of  logarithm subscript 4 baseline 20 .Evaluate both log416 and log44 and show that their product is equal to the value of log464.Evaluate both  logarithm subscript 4 baseline 16  and  logarithm subscript 4 baseline 4  and show that their product is equal to the value of  logarithm subscript 4 baseline 64 .Evaluate both log416 and log44 and show that their product is equal to the value of log420.Evaluate both  logarithm subscript 4 baseline 16  and  logarithm subscript 4 baseline 4  and show that their product is equal to the value of  logarithm subscript 4 baseline 20 .

GPT-4o mini · Answer

To show that the Product Rule of Logarithms works for the base 4 expression \( \log_4 16 + \log_4 4 \), you should evaluate both logarithms and demonstrate that their sum equals \( \log_4 64 \).

Here is the reasoning:

Calculate \( \log_4 16 \):
- Since \( 16 = 4^2 \), we have \( \log_4 16 = 2 \).
Calculate \( \log_4 4 \):
- Since \( 4 = 4^1 \), we have \( \log_4 4 = 1 \).
Now, sum the two results: \[ \log_4 16 + \log_4 4 = 2 + 1 = 3. \]
Calculate \( \log_4 64 \):
- Since \( 64 = 4^3 \), we have \( \log_4 64 = 3 \).
Compare the sums: \[ \log_4 16 + \log_4 4 = 3 = \log_4 64. \]

Thus, option "Evaluate both \( \log_4 16 \) and \( \log_4 4 \) and show that their sum is equal to the value of \( \log_4 64 \)" best describes how to show that the Product Rule of Logarithms works for this expression.