# Which one of the following is not true?

## A. log2 8 = 3 B. log2 1 = 0 C. log2 2 = 1 D. log2 1/8 = -3 E. log2 (-1) = 1/2

Jul 9, 2018

#### Explanation:

Log of a negative number is undefined,

Hence ${\log}_{2} \left(- 1\right)$ is Undefined.

Other explanation:

${\log}_{2} \left(8\right) = {\log}_{2} {\left(2\right)}^{3} = 3 {\log}_{2} \left(2\right) = 3 \to$ A is True

${\log}_{2} \left(1\right) = 0 \to$ B is True. This is a basic log rule.

${\log}_{2} \left(2\right) = 1 \to$ C is True. This is a basic log rule

${\log}_{2} \left(\frac{1}{8}\right) = {\log}_{2} \left(1\right) - {\log}_{2} \left(8\right)$

$= 0 - {\log}_{2} {\left(2\right)}^{3} = 0 - 3 {\log}_{2} \left(2\right) = 0 - 3 = - 3 \to$ D is True