Question

Is the answer log (x sqrt 3/5 ) Which expression represents 1/3 log x-log 5 as a single logarithm?

Answer 1

To simplify the expression \( \frac{1}{3} \log x - \log 5 \) as a single logarithm, we can follow these steps:

We start with:
\[
\frac{1}{3} \log x - \log 5
\]

First, we'll rewrite \( \frac{1}{3} \log x \) using the property of logarithms that states \( a \log b = \log(b^a) \):
\[
\frac{1}{3} \log x = \log(x^{1/3})
\]

Now we can rewrite the expression:
\[
\log(x^{1/3}) - \log 5
\]

Next, we apply the logarithm subtraction rule, which states \( \log a - \log b = \log\left(\frac{a}{b}\right) \):
\[
\log\left(\frac{x^{1/3}}{5}\right)
\]

Thus, the expression \( \frac{1}{3} \log x - \log 5 \) can be represented as a single logarithm:
\[
\log\left(\frac{x^{1/3}}{5}\right)
\]

This is the final simplified form, and it is different from the expression \( \log\left(\frac{x \sqrt{3}}{5}\right) \) you initially asked about.