Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of
base formula. Write the answer rounded to the nearest ten-thousandth.
-
A) 3.9539
B) 1.9036
C) 0.5253
D) 1.2304

Question

Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of
base formula. Write the answer rounded to the nearest ten-thousandth.
-
A) 3.9539 
B) 1.9036 
C) 0.5253 
D) 1.2304

Quizplus · Accepted Answer

Using the change of base formula, we have:

$log_3 2 = \frac{\log 2}{\log 3}$

$log_4 3 = \frac{\log 3}{\log 4}$

$log_2 4 = \frac{\log 4}{\log 2}$

So, our given logarithm can be rewritten as:

$log_2 3 \cdot log_3 2 + log_4 3 - log_2 4 = \frac{\log 3}{\log 2} \cdot \frac{\log 2}{\log 3} + \frac{\log 3}{\log 4} - \frac{\log 4}{\log 2}$

Simplifying this expression, we get:

$log_2 3 \cdot log_3 2 + log_4 3 - log_2 4 = 1 + \frac{\log 3}{\log 4} - 2$

$log_2 3 \cdot log_3 2 + log_4 3 - log_2 4 = \frac{\log 3}{\log 4} - 1$

Using a calculator, we get:

$log_2 3 \cdot log_3 2 + log_4 3 - log_2 4 \approx 0.9036$

Rounding to the nearest ten-thousandth, we get:

$log_2 3 \cdot log_3 2 + log_4 3 - log_2 4 \approx 0.9036$

Therefore, the answer is B. Using the change of base formula, we have:
$\log_{30}(50) = \frac{\log_{10}(50)}{\log_{10}(30)} \approx 1.90361$
Rounding to the nearest ten-thousandth, we get 1.9036. Therefore, the answer is choice B.

Use the Change of Base Formula to Find the Value