Question

Let logb(2) = 0.3869, logb(3) = 0.6131, and logb(5) = 0.8982. Using these values, evaluate logb(1/6).

Answer 1

The value is -1

Explanation:

We use two properties of logarithms: (1) an exponent of the argument can be written as factor of the log, (2) log of a product of two terms is the sum of log of each term:

`\log_b (1)/(6)=\log_b 6^(-1)=-1\cdot \log_b 6=-\log_b(2\cdot 3)=\\= -(\log_b 2 + \log_b 3)=-(0.3869+0.6131)=-1`