Assume that $\log _ { b } 4 = 0.6061$ and $\log _ { b } 9 = 0.9082$ Use these values and properties of logarithms to find $\log _ { b } 36$ . Round your answers to four decimal places.
A) $- 0.3021$
B) 0.3021
C) 0.5505
D) 1.5143

Question

Quizplus · Accepted Answer

The logarithm of 36 in base b can be found by using the property of logarithms that $\log_b(mn) = \log_b(m) + \log_b(n)$. Since $36 = 4 \times 9$, we can use the given values to find $\log_b(36) = \log_b(4) + \log_b(9) = 0.6061 + 0.9082 = 1.5143$.

Assume That log⁡b4=0.6061\log _ { b } 4 = 0.6061logb​4=0.6061 And log⁡b9=0.9082\log _ { b } 9 = 0.9082logb​9=0.9082

Assume That $\log _ { b } 4 = 0.6061$ And $\log _ { b } 9 = 0.9082$