Question

evaluate the following logarithms without a calculator: \\(\log_{5}(25) = \square\\) \\(\log_{3}(1) = \square\\) \\(\log_{2}(8) = \square\\) question help: video

Explanation:

Step1: Evaluate $\log_{5}(25)$

Recall the definition of a logarithm: $\log_{b}(x) = y$ means $b^{y}=x$. For $\log_{5}(25)$, we need to find $y$ such that $5^{y}=25$. Since $5^{2}=25$, then $\log_{5}(25) = 2$.

Step2: Evaluate $\log_{3}(1)$

Using the logarithm definition, $\log_{3}(1)=y$ implies $3^{y}=1$. Any non - zero number to the power of $0$ is $1$, so $3^{0}=1$. Thus, $\log_{3}(1)=0$.

Step3: Evaluate $\log_{2}(8)$

For $\log_{2}(8)=y$, we need $2^{y}=8$. Since $2^{3}=8$, then $\log_{2}(8)=3$.

Answer:

$\log_{5}(25)=\boldsymbol{2}$, $\log_{3}(1)=\boldsymbol{0}$, $\log_{2}(8)=\boldsymbol{3}$