Question

Using numerical analysis and the Quotient Rule of Logarithms, how can log
11
​
(
t
14
​
) be rewritten?
A. log
11
​
14+log
11
​
t
B. log
11
​
(14−t)
C. log
11
​
t−log
11
​
14
D. log
11
​
14−log
11
​
t

Answer 1

To rewrite the expression \( \log_{11}(t^{14}) \) using the properties of logarithms, specifically the Power Rule, we can use the following:

The Power Rule states that \( \log_b(a^n) = n \cdot \log_b(a) \).

In this case, we have:

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

Now, looking at the answer choices provided:

A. \( \log_{11} 14 + \log_{11} t \)

B. \( \log_{11} (14 - t) \)

C. \( \log_{11} t - \log_{11} 14 \)

D. \( \log_{11} 14 - \log_{11} t \)

None of the options seem to represent \( 14 \cdot \log_{11}(t) \) directly.

However, it's important to note that none of the given options are equivalent to \( \log_{11}(t^{14}) \).

Hence, the correct interpretation of \( \log_{11}(t^{14}) \) is simply \( 14 \cdot \log_{11}(t) \) which is not listed among the options provided.

If we must choose from the options given, none of them accurately rewrite \( \log_{11}(t^{14}) \).

Would you like to check again for context or further clarify the problem?