Question

question
evaluate:

(log_{81} 243)

answer attempt 1 out of 2

Explanation:

Step1: Express numbers as powers of 3

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

Step2: Apply logarithm power rule

The power rule of logarithms states that \(\log_{a^m}b^n=\frac{n}{m}\log_ab\). Also, \(\log_aa = 1\), so \(\log_{3^4}3^5=\frac{5}{4}\log_33\). Since \(\log_33 = 1\), we have \(\frac{5}{4}\times1=\frac{5}{4}\).

Answer:

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