Question

Evaluate log ^3square root 100

Answer 1

To evaluate \( \log \sqrt[3]{100} \), we can break down the expression step by step.

First, we express the cube root in terms of a power:

\[
\sqrt[3]{100} = 100^{1/3}
\]

Now, we can utilize the logarithmic identity \(\log(a^b) = b \cdot \log(a)\):

\[
\log \sqrt[3]{100} = \log(100^{1/3}) = \frac{1}{3} \log(100)
\]

Next, we evaluate \( \log(100) \). Since \(100\) can be expressed as \(10^2\):

\[
\log(100) = \log(10^2) = 2 \cdot \log(10)
\]

If we assume base 10 for the logarithm, then \(\log(10) = 1\):

\[
\log(100) = 2 \cdot 1 = 2
\]

Now, substituting this back into our earlier expression:

\[
\log \sqrt[3]{100} = \frac{1}{3} \cdot 2 = \frac{2}{3}
\]

Thus, the final result is:

\[
\log \sqrt[3]{100} = \frac{2}{3}
\]