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Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

[tex]\[
\log_b x^3
\][/tex]

[tex]\[
\log_b x^3 =
\][/tex]

Sagot :

GinnyAnsweridn
Let's expand the given logarithmic expression [tex]\(\log_b(x^3)\)[/tex] step-by-step using properties of logarithms:

1. Identify the rule applicable: The given expression is [tex]\(\log_b(x^3)\)[/tex]. For logarithmic expressions involving exponents, we can use the power rule of logarithms. The power rule states that [tex]\(\log_b(x^n) = n \cdot \log_b(x)\)[/tex].

2. Apply the power rule: In our expression, the exponent [tex]\(n\)[/tex] is 3. By applying the power rule, we can rewrite the expression as:
[tex]\[ \log_b(x^3) = 3 \cdot \log_b(x) \][/tex]

Therefore, the expanded logarithmic expression is:
[tex]\[ 3 \cdot \log_b(x) \][/tex]

In conclusion, [tex]\(\log_b(x^3)\)[/tex] simplifies to [tex]\(3 \cdot \log_b(x)\)[/tex] when expanded using the properties of logarithms.
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