Solve 23x 3 middot 22x 2x 3Solution23x 3 22x 2x 3 lets

Solve: 2^3x + 3 middot 2^2x - 2^x = 3

Solution

2^3x + 3* 2^2x - 2^x = 3

let\'s substitute

2^x = y

now the equation becomes

y^3 + 3y^2 - y = 3

subtracting 3 from both sides

y^3 + 3y^2 - y - 3 = 0

on solving we get

y = 1

y = -1

y = -3

since y = 2^x

1 = 2^x

taking natural log on both sides

ln 1 = x ln 2

x = ln 1 / ln 2 = 0

y = -1

x = ln -1 / ln 2 ( negative log does not exists)

therefore, there is only one solution

x = 0