ICSE BoardEnglish MediumSTD 9MATHEMATICSLogarithms1 Mark
Question
State, true or false : $\log _2 8=3$ and $\log _8=2=\frac{1}{3}$
✓
Answer
Consider the equation $ \log _2 8=3 $ $\Rightarrow 2^3=8$ $\ldots(1)$ Now consider the equation $ \begin{aligned} & \log _8 2=\frac{1}{3} \\ & \Rightarrow 8^{\frac{1}{3}}=2 \end{aligned} $ $\Rightarrow\left(2^3\right)^{\frac{1}{3}}=2$ $\ldots(2)$ Both the equations (1) and (2) are correct. Thus the given statements, $\log _2 8=3$ and $\log _8 2=\frac{1}{3}$ are true.
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