Which one of the following is not true?

Question

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

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Answer 1 · 2018-07-09T06:19:10

The answer is E.

Log of a negative number is undefined,

Hence ${log}_{2} (- 1)$ $log_2 (-1)$ is Undefined.

The answer is E.

Other explanation:

${log}_{2} (8) = {log}_{2} {(2)}^{3} = 3 {log}_{2} (2) = 3 \to$ $log_2 (8) = log_2(2)^3 = 3log_2(2) = 3 ->$ A is True

${log}_{2} (1) = 0 \to$ $log_2 (1) = 0 ->$ B is True. This is a basic log rule.

${log}_{2} (2) = 1 \to$ $log_2(2) = 1 ->$ C is True. This is a basic log rule

${log}_{2} (\frac{1}{8}) = {log}_{2} (1) - {log}_{2} (8)$ $log_2 (1/8) = log_2(1) - log_2(8)$

$= 0 - {log}_{2} {(2)}^{3} = 0 - 3 {log}_{2} (2) = 0 - 3 = - 3 \to$ $= 0 - log_2(2)^3 = 0-3log_2(2) = 0-3 = -3 ->$ D is True