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]
