Question

find the exact value of the logarithm without using a calculator.
\\(\log _{12}144\\)

\\(\log _{12}144 = \square\\)
(type an integer or a simplified fraction.)

Explanation:

Step1: Recall the logarithm definition

The logarithm \(\log_{b}a = x\) is equivalent to \(b^{x}=a\). So for \(\log_{12}144\), we need to find \(x\) such that \(12^{x}=144\).

Step2: Express 144 as a power of 12

We know that \(12\times12 = 12^{2}=144\). So comparing with \(12^{x}=144\), we see that \(x = 2\).

Answer:

2