Quadratic equation

Solve the equation

2^2x – 2^x – 6 = 0

Answer

Take,  2^x = y

So, y² – y – 6 = 0

Or, y² – 3y + 2y – 6 = 0

Or, y (y – 3) + 2(y – 3) = 0

Or, (y + 2)(y – 3) = 0

So, y = -2, 3

Now 2^x = y = -2 is not possible.

So, 2^x = y = 3

Taking log on both sides,

xlog2 = log3

So, x = log3/log2