Question

Rewrite f(x)=log(x/100−1/10)
using the properties of logarithms.(1 point)
f(x)=log
(
)−

Answer 1

To rewrite the function \( f(x) = \log\left(\frac{x}{100} - \frac{1}{10}\right) \) using properties of logarithms, we first need to simplify the expression inside the log function.

First, we can express \( \frac{1}{10} \) in terms of a common denominator with \( \frac{x}{100} \):

\[
\frac{1}{10} = \frac{10}{100}
\]

Thus, we can rewrite the expression inside the log:

\[
\frac{x}{100} - \frac{1}{10} = \frac{x}{100} - \frac{10}{100} = \frac{x - 10}{100}
\]

Now, we substitute this back into the logarithm:

\[
f(x) = \log\left(\frac{x - 10}{100}\right)
\]

Using the properties of logarithms, specifically the quotient rule \( \log\left(\frac{a}{b}\right) = \log(a) - \log(b) \), we can split this into two logarithmic expressions:

\[
f(x) = \log(x - 10) - \log(100)
\]

Since \( \log(100) = 2 \) (because \( 100 = 10^2 \)), we can finally express \( f(x) \) as:

\[
f(x) = \log(x - 10) - 2
\]

So, the final answer is:

\[
f(x) = \log(x - 10) - 2
\]