Question

what is the value of \\(\log_{3} 81\\)?

Explanation:

Step1: Recall the definition of logarithm

The logarithm \(\log_{b}a\) is the exponent \(x\) such that \(b^{x}=a\). So we need to find \(x\) where \(3^{x} = 81\).

Step2: Express 81 as a power of 3

We know that \(3^{4}=81\) (since \(3\times3\times3\times3 = 81\)).

Step3: Relate to the logarithm definition

From the definition of logarithm, if \(3^{x}=81\) and \(3^{4}=81\), then \(x = 4\). So \(\log_{3}81=4\).

Answer:

4