Question
write in simplest form 4 log(b) 3
Answers
GPT-4o mini
To simplify the expression \( 4 \log(b) 3 \), we can use the property of logarithms that allows us to move the coefficient in front of the logarithm as a power of the argument.
Specifically, the property states:
\[
a \log_b(x) = \log_b(x^a)
\]
Applying this to your expression:
\[
4 \log(b) 3 = \log(b)(3^4) = \log(b) 81
\]
So, the simplest form of \( 4 \log(b) 3 \) is:
\[
\log(b) 81
\]
Specifically, the property states:
\[
a \log_b(x) = \log_b(x^a)
\]
Applying this to your expression:
\[
4 \log(b) 3 = \log(b)(3^4) = \log(b) 81
\]
So, the simplest form of \( 4 \log(b) 3 \) is:
\[
\log(b) 81
\]