Question

question 3 of 10
evaluate the following expression. round your answer to two decimal places.
\\(\log_{3} 10\\)
a. 0.48
b. 2.10
c. 0.76
d. 2.30

Explanation:

Step1: Use Change of Base Formula

The change of base formula for logarithms is $\log_b a = \frac{\log_c a}{\log_c b}$ (we can use $c = 10$ or $c = e$). So, $\log_3 10=\frac{\log 10}{\log 3}$.

Step2: Calculate Logarithms

We know that $\log 10 = 1$ (since $\log_{10} 10 = 1$) and $\log 3\approx0.4771$. Then $\frac{1}{0.4771}\approx2.095$.

Step3: Round to Two Decimal Places

Rounding $2.095$ to two decimal places gives $2.10$.

Answer:

B. 2.10