Answer :
To rewrite the expression [tex]\(2 \log (3)\)[/tex] in the form [tex]\(\log (c)\)[/tex], we can use one of the properties of logarithms known as the power rule. The power rule states that for any positive real number [tex]\(a\)[/tex] and any real number [tex]\(b\)[/tex],
[tex]\[ b \log (a) = \log (a^b). \][/tex]
In our case, we have [tex]\(2 \log (3)\)[/tex]. Applying the power rule where [tex]\(a = 3\)[/tex] and [tex]\(b = 2\)[/tex], we get:
[tex]\[ 2 \log (3) = \log (3^2). \][/tex]
Next, we need to evaluate [tex]\(3^2\)[/tex]:
[tex]\[ 3^2 = 9. \][/tex]
Therefore, we can rewrite [tex]\(2 \log (3)\)[/tex] as:
[tex]\[ \log (3^2) = \log (9). \][/tex]
So, [tex]\(c = 9\)[/tex] and the expression [tex]\(2 \log (3)\)[/tex] can be rewritten as [tex]\(\log (9)\)[/tex].
[tex]\[ b \log (a) = \log (a^b). \][/tex]
In our case, we have [tex]\(2 \log (3)\)[/tex]. Applying the power rule where [tex]\(a = 3\)[/tex] and [tex]\(b = 2\)[/tex], we get:
[tex]\[ 2 \log (3) = \log (3^2). \][/tex]
Next, we need to evaluate [tex]\(3^2\)[/tex]:
[tex]\[ 3^2 = 9. \][/tex]
Therefore, we can rewrite [tex]\(2 \log (3)\)[/tex] as:
[tex]\[ \log (3^2) = \log (9). \][/tex]
So, [tex]\(c = 9\)[/tex] and the expression [tex]\(2 \log (3)\)[/tex] can be rewritten as [tex]\(\log (9)\)[/tex].
