Question

Rewrite the logarithm log 10^4/5

Answer 1

To rewrite the logarithm \( \log \frac{10^4}{5} \), you can use the properties of logarithms. Specifically, you can apply the quotient rule, which states that \( \log \frac{a}{b} = \log a - \log b \).

Here's the step-by-step rewrite:

\[
\log \frac{10^4}{5} = \log(10^4) - \log(5)
\]

Next, we can simplify \( \log(10^4) \) using the power rule, which states that \( \log(a^b) = b \log(a) \):

\[
\log(10^4) = 4 \log(10)
\]

Since \( \log(10) = 1 \):

\[
4 \log(10) = 4
\]

So, we substitute this into the logarithmic expression:

\[
\log \frac{10^4}{5} = 4 - \log(5)
\]

Thus, the rewritten form of \( \log \frac{10^4}{5} \) is:

\[
4 - \log(5)
\]