Expert answers to "How do you evaluate log2166?"

Lyric Morris

Answered question

2022-02-01

How do you evaluate

\log_{216} 6 ?

Alvaro Pollard

Beginner2022-02-02Added 16 answers

Step 1

6^{2} = 36

6^{3} = 36 \times 6 = 180 + 36 = 216

216^{\frac{1}{3}} = 6

and

\log_{216} 6 = \frac{1}{3}

iluvyou23452nwj

Beginner2022-02-03Added 19 answers

Step 1
By

\log

rule

\log_{a} (n) = \frac{\log n}{\log a}

\log_{216} (6) = \frac{\log 6}{\log 216} = \frac{\log (6^{1})}{\log (6^{3})}

Now use the rule

\log (a^{n}) = n \log a

and simplify:

= \frac{1 \log 6}{3 \log 6}

= \frac{1}{3}

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