​ Logarithmic form of ^{3}√8 = 2 is ​

Question

Logarithmic form of \(\sqrt[3]{8}\) = 2 is

A) log₈ 2 = 1/3

B) log₂ 8 = 1/3

C) log_1/3 8 = 2

D) log_1/3 2 = 0

Answer 1

Correct option is (A) log₈ 2 = 1/3

\(\sqrt[3]8\) = 2

i.e., \((8)^\frac13\) = 2

\(\Rightarrow\) \(log_8\,(8)^\frac13\) \(=log_8\,2\)   (By taking \(log_8\) both sides)

\(\Rightarrow\) \(\frac13\,log_8\,8\) \(=log_8\,2\)

\(\Rightarrow\) \(log_8\,2\) \(=\frac13\)    \((\because log_8\,8=1)\)

Answer 2

Correct option is log ₈ 2 = 1/3