Solve the exponential equation

Question

1. Solve the exponential equation 4^x + 2^x+1 – 24 = 0

Answer 1

The given equation is equivalent to (2^x)² + 2(2^x) - 24 = 0

If we let u = 2^x, then u² + 2u - 24 = 0

So, (u + 6)(u - 4) = 0

Thus, u = -6 or u = 4

That is, 2^x = -6 or 2^x = 4

The equation 2^x = -6 has no solution since 2^x is positive for all x.

So, 2^x = 4. Therefore, x = 2

Answer 2

Using Newton’s iterative method, the answer converges quickly to. X = 2