Using numerical analysis and the Quotient Rule of Logarithms, how can log11(14/t)

Question

be rewritten?(1 point)
Responses

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

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

log1114−log11

Answer 1

To rewrite \( \log_{11}\left( \frac{14}{t} \right) \) using the Quotient Rule of Logarithms, we can apply the rule, which states that:

\[ \log_b\left(\frac{a}{c}\right) = \log_b(a) - \log_b(c) \]

Applying this rule to \( \log_{11}\left( \frac{14}{t} \right) \):

\[ \log_{11}\left( \frac{14}{t} \right) = \log_{11}(14) - \log_{11}(t) \]

Therefore, the correct answer is:

log11(14) - log11(t)

So from the options provided, it should be written as:

log11t − log1114

This is the correct choice which matches that structure if you reverse the terms.