Question

question
what is the value of \\(\log_{6} 36\\)?

answer attempt 1 out of 2

Explanation:

Step1: Recall logarithm definition

The logarithm \(\log_{b}a = x\) means \(b^{x}=a\). For \(\log_{6}36\), let \(x = \log_{6}36\), so we need to find \(x\) such that \(6^{x}=36\).

Step2: Express 36 as a power of 6

We know that \(36 = 6^{2}\). So the equation \(6^{x}=36\) becomes \(6^{x}=6^{2}\).

Step3: Solve for x

Since the bases are the same (\(b = 6\) for \(b^{x}=b^{2}\)), the exponents must be equal. Thus, \(x = 2\).

Answer:

2