Question

2^m - 2^m-1 -4 = 0.Find m​

Answer 1

${2}^{m} - {2}^{m - 1} - 4 = 0$

${2}^{m} - {2}^{m - 1} = 4$

${2}^{m - 1} (2 - 1) = 4$

${2}^{m - 1} = 4$

${2}^{m - 1} = {2}^{2}$

Equating the exponents when base is same,

=> m - 1 = 2

$= > \fbox{m = 3}$

Hence, the magnitude of m satisfying the given equation is m = 3.

Answer 2

${2}^{m} - {2}^{m - 1} - 4 = 0$

Or,

${2}^{m - 1} (2 - 1) = 4$

Or,

${2}^{m - 1} = 4$

Or,

$2^{m - 1} = {2}^{2}$

Or,

$m - 1 = 2$

Or,

$m = 3$

Hence, the required value of m is 3.

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