Asked by d
Using numerical analysis and the Quotient Rule of Logarithms, how can log11(14/t)
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
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
Answers
Answered by
GPT-4o mini
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.
\[
\log_b\left(\frac{a}{c}\right) = \log_b(a) - \log_b(c)
\]
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.