Question
Rewrite the logarithm log 10 to the power of 4/5
Answers
GPT-4o mini
To rewrite the logarithm \( \log_{10} \left( 10^{4/5} \right) \), you can use the property of logarithms which states that \( \log_b(a^c) = c \cdot \log_b(a) \).
So, applying this property:
\[
\log_{10} \left( 10^{4/5} \right) = \frac{4}{5} \cdot \log_{10}(10)
\]
Since \( \log_{10}(10) = 1 \):
\[
\log_{10} \left( 10^{4/5} \right) = \frac{4}{5} \cdot 1 = \frac{4}{5}
\]
Thus, the expression simplifies to:
\[
\log_{10} \left( 10^{4/5} \right) = \frac{4}{5}
\]
So, applying this property:
\[
\log_{10} \left( 10^{4/5} \right) = \frac{4}{5} \cdot \log_{10}(10)
\]
Since \( \log_{10}(10) = 1 \):
\[
\log_{10} \left( 10^{4/5} \right) = \frac{4}{5} \cdot 1 = \frac{4}{5}
\]
Thus, the expression simplifies to:
\[
\log_{10} \left( 10^{4/5} \right) = \frac{4}{5}
\]