Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places.
-$\log _ { 3,9 } 10$
A) 1.69
B) 1.00
C) 2.56
D) 0.59

Question

Quizplus · Accepted Answer

The Change-of-Base Formula allows us to rewrite the logarithm in a base that our calculator can understand, typically base 10 or base e. For this problem, we can use the formula $\log_b a = \frac{\log_c a}{\log_c b}$, where $b$ is the original base (in this case, 3.9), $a$ is the value we're taking the logarithm of (in this case, 10), and $c$ is the new base we're converting to (commonly 10 or e). Using base 10, we get $\log_{3.9} 10 = \frac{\log_{10} 10}{\log_{10} 3.9}$. Using a calculator, this evaluates to approximately 1.69 when rounded to two decimal places.

Use the Change-Of-Base Formula and a Calculator to Evaluate the Logarithm