Question

evaluate the logarithmic expression: $log_{4}(256)$

Explanation:

Step1: Recall the logarithm definition

The logarithm \(\log_{b}(a)\) is the exponent \(x\) such that \(b^{x}=a\). So we need to find \(x\) where \(4^{x} = 256\).

Step2: Express 256 as a power of 4

We know that \(4^{1}=4\), \(4^{2} = 16\), \(4^{3}=64\), \(4^{4}=256\) (since \(4\times4 = 16\), \(16\times4=64\), \(64\times4 = 256\)). So \(x = 4\) when \(4^{x}=256\).

Answer:

\(4\)