Question

solve the equation 2^x-3=4^x-1

Answer 1

Step-by-step explanation:

${2}^{x - 3} = {4}^{x - 1} \\ {2}^{x - 3} = {( {2}^{2} )}^{x - 1} \\ {2}^{x - 3} = {2}^{2x - 2} \\ base \: are \: same \: powers \: to \: be \: equated \\ x - 3 = 2x - 2 \\ x - 2x = - 2 + 3 \\ - x = 1 \\ x = - 1$

therefore x = -1

verification

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

Hope you get your answer