Question

Find the value of X :-
2^x + 2^x +2^x = 192

Answer 1

3×2^x=192
2^x=64
2^x=2^6
By equalizing the base
x=6

Answer 2

${2}^{x} + {2}^{x} + {2}^{x} = 192 \\ \\ Take \: \: {2}^{x} \: \: as \: \: common \\ \\ {2}^{x} (1 + 1 + 1) = 192 \\ \\ {2}^{x} \times 3 = 192 \\ \\ {2}^{x} = \frac{192}{3} \\ \\ {2}^{x} = 64 \\ \\ Factorise \: \: 64 \\ 64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = {(2)}^{6} \\ \\ {2}^{x} = {2}^{6} \\ \\ Bases \: \: are \: \: same \: \: now \: \\ equating \: \: their \: \: powers \\ \\ x = 6 \\ \\ \\ V arification \\ L.H.S = \: \: {2}^{x} + {2}^{x} + {2}^{x} \\ \\ {2}^{6 } + {2}^{6 } + {2}^{6 } \\ \\ 64 + 64 + 64 = 192 = R.H.S$