Question

solve 2powerX+1 =4PowerX-1

Answer 1

Heya dear user !!!

Here is your answer,

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${(2)}^{x + 1} = {(4)}^{x - 1} \\ \\ {(2)}^{x + 1} = {(2)}^{2 \times (x - 1)} \\ \\ {(2)}^{x + 1} = {(2)}^{2x - 2} \\ \\ bases \: \: are \: \: same \: \\ now \: \: equating \: \: their \: \: powers \\ \\ x + 1 = 2x - 2 \\ \\ 1 + 2 = 2x - x \\ \\ 3 = 1x$

Hence, x = 1

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Verification
$L.H.S = {(2)}^{x + 1} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = {(2)}^{3 + 1} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = {(2)}^{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 2 \times 2 \times 2 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = 16 \\ \\ R.H.S = {(4)}^{x - 1} \\ \\ \: \: \: \: \: \: \: \: \: \: \: = {(4)}^{3 - 1} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = {(4)}^{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = 4 \times 4 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = 16$

Hence, L.H.S = R.H.S ( verified )

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Hope it helps.