Question

Question
Using numerical analysis and the Quotient Rule of Logarithms, how can log11(14t)
be rewritten?(1 point)
Responses

log11(14−t)
logarithm subscript 11 baseline left parenthesis 14 minus t right parenthesis

log1114+log11t
logarithm subscript 11 baseline 14 plus logarithm subscript 11 baseline t

log11t−log1114
logarithm subscript 11 baseline t minus logarithm subscript 11 baseline 14

log1114−log11t
logarithm subscript 11 baseline 14 minus logarithm subscript 11 baseline t

Answer 1

To rewrite \( \log_{11}(14t) \) using the Quotient Rule of Logarithms, we utilize the property that states:

\[
\log_b(mn) = \log_b(m) + \log_b(n)
\]

In this case, \( m = 14 \) and \( n = t \), so we can apply the rule as follows:

\[
\log_{11}(14t) = \log_{11}(14) + \log_{11}(t)
\]

Thus, the correct answer is:

\[
\log_{11}(14) + \log_{11}(t)
\]

So the answer from the provided responses is:

**log1114 + log11t**
(logarithm subscript 11 baseline 14 plus logarithm subscript 11 baseline t)