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For any positive numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(d\)[/tex], with [tex]\(b \neq 1\)[/tex], [tex]\(\log_b\left(a^d\right) =\)[/tex]

A. [tex]\(d \cdot \log_b a\)[/tex]

B. [tex]\(\log_b a + \log_b d\)[/tex]

C. [tex]\(a^d + \log_b a^d\)[/tex]

D. [tex]\(d + \log_b a\)[/tex]

Sagot :

GinnyAnsweridn
To answer the question about simplifying [tex]\(\log_b\left(a^9\right)\)[/tex], let's review the properties of logarithms. Specifically, we will use the power rule of logarithms.

The power rule states:
[tex]\[ \log_b(a^d) = d \cdot \log_b(a) \][/tex]

In our case, we have:
[tex]\[ \log_b(a^9) \][/tex]

By applying the power rule to this expression, we get:
[tex]\[ \log_b(a^9) = 9 \cdot \log_b(a) \][/tex]

So, the simplified form of the given expression is:
[tex]\[ 9 \cdot \log_b(a) \][/tex]

Thus, the correct answer is:
[tex]\[ \boxed{A. \, 9 \cdot \log_b(a)} \][/tex]
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