Which of the following rewritten logarithms uses the Power Rule of Logarithms to evaluate log104/5

?(1 point)
Responses

−4/5 log10
negative Start Fraction 4 over 5 End Fraction

−5/4 log10
negative Start Fraction 5 over 4 End Fraction

5/4 log10
Start Fraction 5 over 4 End Fraction

4/5 log10
Start Fraction 4 over 5 End Fraction

1 answer

To apply the Power Rule of Logarithms, you can rewrite a logarithm in the form \( \log_b(a^n) = n \cdot \log_b(a) \).

Given the expression \( \log_{10} \left( \frac{4}{5} \right) \), we notice that we can express it using the property of logarithms:

\[ \log_{10} \left( \frac{4}{5} \right) = \log_{10}(4) - \log_{10}(5) \]

However, none of the options provided directly represent this operation. The Power Rule typically applies when you have a logarithm of a power, which is not the case here without modifying the expression further.

Thus, the logarithm would need to be rewritten in a form that utilizes exponents, which would reflect the Power Rule more directly.

If we were to analyze the options as potential outputs of rewriting \( \log_{10} \left( \frac{4}{5} \right) \), none fit correctly under the explicit use of the Power Rule, since we cannot simply convert \( \frac{4}{5} \) into an exponent without additional context.

Considering the standard Power Rule application might lead to a misunderstanding. Therefore, none of the options listed seems to be a valid transformation of \( \log_{10} \left( \frac{4}{5} \right) \) using just the Power Rule.

Let me know if there is anything specific you were looking for in the explanation or a different aspect of logarithms you wish to explore!