How do you evaluate log_7 7^3?

1 Answer
Mar 6, 2018

"The result is:" \qquad \qquad \qquad \quad log_{7} 7^3 \ = \ 3.

Explanation:

"We can evaluate this by using the Rules for Logarithms --"
"it may go faster than you think ... "

\qquad \qquad \qquad \qquad log_{7} 7^3 \ = \ log_{7} 7^color{red}{3}

\qquad \qquad \qquad \qquad \qquad \qquad \qquad = \ color{red}{3} cdot log_{7} 7 \qquad color{blue}{"use Power Rule for Logarithms:"}
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \ color{blue}{ log_{b} x^color{red}{p} \ = \ color{red}{p} cdot log_{b} x \quad. }

\qquad \qquad \qquad \qquad \qquad \qquad \qquad = \ 3 cdot 1 \qquad \qquad \quad \ \ color{blue}{"use Basic Rule for Logarithms:"}
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \ \ color{blue}{ log_{b} b \ = \ 1 \quad. }

\qquad \qquad \qquad \qquad \qquad \qquad \qquad = \ 3.

"Done !!"

"So we have our result:"

\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \ \ log_{7} 7^3 \ = \ 3.