Which option best describes how to show that the Quotient Rule of Logarithms works for the base 2 expression log216−log28

Question

?

Option #1: Evaluate both log216
and log28
and show that their difference is equal to the value of log22
.

Option #2: Evaluate both log216
and log28
and show that their difference is equal to the value of log28
.

Option #3: Evaluate both log216
and log28
and show that their quotient is equal to the value of log22
.

Option #4: Evaluate both log216
and log28
and show that their quotient is equal to the value of log28
.

(1 point)
The option that best describes how to show that the Quotient Rule of Logarithms works for the base 2 expression log216−log28
is Option #
.
Remaining Attempts : 3
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Answer 1

To show that the Quotient Rule of Logarithms works for the expression \( \log_2 16 - \log_2 8 \), you would ideally want to demonstrate that the difference of the two logarithms equals the logarithm of the quotient of the two corresponding numbers, i.e.,

\[ \log_2 16 - \log_2 8 = \log_2 \left(\frac{16}{8}\right) \]

Since \( \frac{16}{8} = 2 \), this means you want to show that:

\[ \log_2 16 - \log_2 8 = \log_2 2 \]

Evaluating each logarithm:

• \( \log_2 16 = 4 \) (since \( 2^4 = 16 \))
• \( \log_2 8 = 3 \) (since \( 2^3 = 8 \))

Now, calculate:

\[ \log_2 16 - \log_2 8 = 4 - 3 = 1 \]

And since \( \log_2 2 = 1 \):

\[ \log_2 16 - \log_2 8 = \log_2 2 \]

Therefore, the option that best describes how to show that the Quotient Rule of Logarithms works for the base 2 expression \( \log_2 16 - \log_2 8 \) is:

Option #1: Evaluate both \( \log_2 16 \) and \( \log_2 8 \) and show that their difference is equal to the value of \( \log_2 2 \).