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. #