Question 177(iii)

Find x.
$2^{x} + 2^{x} + 2^{x} = 192$

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Solution

We have, $2^{x} + 2^{x} + 2^{x} = 192 \Rightarrow 2^{x} (1 + 1 + 1) = 192 \Rightarrow 3 \times (2^{x}) = 192 \Rightarrow 2^{x} = \frac{192}{3} = 64 \Rightarrow 2^{x} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \Rightarrow 2^{x} = 2^{6}$
Since, the base is same on both sides, we can equate the powers.
On equating the powers of 2, we get x = 6

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Question 177(iii)

Find x.
$2^{x} + 2^{x} + 2^{x} = 192$

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