Question

evaluate logarithms (level 3) unique id: 0063
score: 2/4 penalty: 0.25 off
question
evaluate:
\\(\log_{243} 81\\)
answer attempt 1 out of 2

Explanation:

Step1: Express numbers as powers of 3

We know that \(243 = 3^5\) and \(81 = 3^4\). So we can rewrite the logarithm \(\log_{243} 81\) as \(\log_{3^5} 3^4\).

Step2: Apply logarithm power rule

The power rule of logarithms states that \(\log_{a^m} b^n=\frac{n}{m}\log_{a} b\). Also, \(\log_{a} a = 1\). So \(\log_{3^5} 3^4=\frac{4}{5}\log_{3} 3\). Since \(\log_{3} 3 = 1\), we have \(\frac{4}{5}\times1=\frac{4}{5}\).

Answer:

\(\frac{4}{5}\)