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Which properties would you use to simplify the following expression?

[tex]\[
\log (17 x^3)
\][/tex]

[tex]\[\square\][/tex]

Sagot :

GinnyAnswer
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]
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