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Use the Laws of Logarithms to expand the expression.

[tex]\[ \log_3(5x) \][/tex]

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

Sagot :

GinnyAnswer
Certainly! Let's expand the given logarithmic expression [tex]\(\log_3(5x)\)[/tex] using the laws of logarithms.

The Law of Logarithms that we will use is the Product Rule, which states:
[tex]\[ \log_b(M \cdot N) = \log_b(M) + \log_b(N) \][/tex]
In this case, [tex]\(M = 5\)[/tex] and [tex]\(N = x\)[/tex].

Applying the product rule to the given expression [tex]\(\log_3(5x)\)[/tex], we get:
[tex]\[ \log_3(5x) = \log_3(5) + \log_3(x) \][/tex]

Thus, the expanded form of the expression [tex]\(\log_3(5x)\)[/tex] is:
[tex]\[ \log_3(5) + \log_3(x) \][/tex]

So the expanded expression is:
[tex]\[ \boxed{\log_3(5) + \log_3(x)} \][/tex]
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