To simplify the given expression [tex]\(\log \left(17 x^3\right)\)[/tex], we will use two important properties of logarithms:
1. Product Rule for Logarithms: [tex]\(\log(a \cdot b) = \log(a) + \log(b)\)[/tex]
2. Power Rule for Logarithms: [tex]\(\log(a^b) = b \log(a)\)[/tex]
Let's apply these properties step-by-step:
1. Apply the Product Rule:
[tex]\[
\log \left(17 x^3\right) = \log(17) + \log(x^3)
\][/tex]
2. Apply the Power Rule to the second term [tex]\(\log(x^3)\)[/tex]:
[tex]\[
\log(x^3) = 3 \log(x)
\][/tex]
Therefore, substituting back, we have:
[tex]\[
\log \left(17 x^3\right) = \log(17) + 3 \log(x)
\][/tex]
So, the simplified expression is:
[tex]\[
\boxed{\log(17) + 3 \log(x)}
\][/tex]
