Question

1. evaluate the logarithm. \\(\log_{3}81 = \square\\)

Explanation:

Step1: Recall the definition of logarithm

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

Step2: Express 81 as a power of 3

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

Step3: Compare with the logarithmic equation

From \(3^{x}=81\) and \(3^{4}=81\), we can see that \(x = 4\). So \(\log_{3}81=4\).

Answer:

4