Question

2^2x+1=4^2x-1 solve the given exponential equation​

Answer 1

Answer:

${2}^{2x + 1} = {4}^{2x - 1} \\ = > {2}^{2x + 1} = {(2)}^{2 \times (2x - 1)} \\ = > {2}^{2x + 1} = {2}^{4x - 2} \\ = > 2x + 1 = 4x - 2 \: \: \: (as \: base \: is \: same) \\ = > 2x - 4x = - 2 - 1 \\ = > - 2x = - 3 \\ = > x = \frac{ - 3}{ - 2} \\ = > x = \frac{3}{2} \: \: ans.$

Answer 2

${2}^{2x + 1} = {4}^{2x - 1} \\ {2}^{2x + 1} = ({ {2} ^{2} })^{2x - 1} \\ {2}^{2x + 1} = {2}^{4x - 2} \\ 2x + 1 = 4x - 2 \\ 2x - 4x = - 2 - 1 \\ - 2x = - 3 \\ x = \frac{3}{2}$