Question

evaluate the logarithmic expression: \\(\log_{5}(625)\\)

Explanation:

Step1: Recall the logarithm definition

The logarithm $\log_{b}(a)$ is the exponent $x$ such that $b^{x}=a$. So for $\log_{5}(625)$, we need to find $x$ where $5^{x}=625$.

Step2: Express 625 as a power of 5

We know that $5^{4}=5\times5\times5\times5 = 625$.

Step3: Determine the exponent

Since $5^{4}=625$, by the definition of logarithms, $x = 4$ when $5^{x}=625$. So $\log_{5}(625)=4$.

Answer:

4