Question

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

Answer 1

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

The term \( \frac{x}{100} - \frac{1}{10} \) can be rewritten with a common denominator:

1. The common denominator for 100 and 10 is 100. So, we can express \( \frac{1}{10} \) as \( \frac{10}{100} \). Thus:

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

Now substituting this back into the function \( f(x) \):

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

Using the properties of logarithms, specifically \( \log\left(\frac{a}{b}\right) = \log(a) - \log(b) \), we can break this down further:

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

Since \( \log(100) = \log(10^2) = 2 \log(10) = 2 \) (assuming the logarithm is base 10), we can express it as:

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

Thus, the rewritten form of \( f(x) \) is:

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