Which option best describes how to show that the Product Rule of Logarithms works for the base 4 expression log416+log44

?(1 point)
Responses

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 .

Evaluate 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 .

1 answer

To demonstrate how the Product Rule of Logarithms works for the expression \( \log_4{16} + \log_4{4} \), we need to show that this sum is equal to the logarithm of the product of the two values. According to the Product Rule, we have:

\[ \log_b{A} + \log_b{B} = \log_b{(A \cdot B)} \]

In your example, we want to evaluate \( \log_4{16} + \log_4{4} \) and show that it equals \( \log_4{(16 \cdot 4)} \), which simplifies to \( \log_4{64} \).

So the option that best describes this process is:

Evaluate both \( \log_4{16} \) and \( \log_4{4} \) and show that their sum is equal to the value of \( \log_4{64} \).