Question 22

Which power of 8 is equal to $2^{6}$ ?
(a) 3
(b) 2
(c) 1
(d) 4

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Solution

Let power of 8 be x.
According to the equation,
$8^{x} = 2^{6} \Rightarrow (2^{3})^{x} = 2^{6} [∵ 8 = 2 \times 2 \times 2 = 2^{3}] \Rightarrow 2^{3 x} = 2^{6} [∵ (a^{m})^{n} = a^{m \times n}])$
Since, base are equal, then by equating their exponents, we get
$3 x = 6$
$\Rightarrow \frac{3 x}{3} = \frac{6}{3} \Rightarrow x = 2$
Hence, the power of 8 is 2, which is equal to $2^{6}$ .

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