Question

lesson 25 - logarithmic functions and equations
score: 0/100 answered: 0/19
question 1
evaluate the following logarithms without a calculator:
\\(\log_{5}(125) = \\)
\\(\log_{3}(81) = \\)
\\(\log_{2}(2) = \\)

Explanation:

Step1: Evaluate $\log_{5}(125)$

Recall the definition of a logarithm: $\log_{b}(x) = y$ means $b^{y}=x$. For $\log_{5}(125)$, we need to find $y$ such that $5^{y}=125$. Since $5^{3}=125$ (because $5\times5\times5 = 125$), so $\log_{5}(125)=3$.

Step2: Evaluate $\log_{3}(81)$

Using the logarithm definition, find $y$ where $3^{y}=81$. We know that $3^{4}=81$ (since $3\times3\times3\times3 = 81$), so $\log_{3}(81)=4$.

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

By the logarithm definition, find $y$ such that $2^{y}=2$. Clearly, $y = 1$ because $2^{1}=2$, so $\log_{2}(2)=1$.

Answer:

$\log_{5}(125)=\boldsymbol{3}$, $\log_{3}(81)=\boldsymbol{4}$, $\log_{2}(2)=\boldsymbol{1}$