Solve.
-Given logb 4 = 1.079 and logb 12 = 1.934, evaluate logb 3.
A) 3.013
B) 0.855
C) 1.792
D) cannot be found using the properties of logarithms

Question

Quizplus · Accepted Answer

Using the properties of logarithms, specifically the quotient rule which states that logb(x/y) = logb(x) - logb(y), we can find logb(3) by rearranging the given information. Since 12 can be expressed as 4*3, logb(12) = logb(4*3). Using the product rule, this can be rewritten as logb(4) + logb(3). We know logb(4) = 1.079 and logb(12) = 1.934. So, 1.934 = 1.079 + logb(3). Solving for logb(3), we get logb(3) = 1.934 - 1.079 = 0.855.

Solve. -Given Logb 4 = 1.079 and Logb 12 = 1.934