Question

How do you solve `3^(x^2) + 4x = 1/27`?

Answer 1

`x approx -1.2, -0.26`

Explanation:

This is called a transcendental equation and therefore does not generally have a simple/exact solution. This is because of the x in the exponential and the coefficient. For example, `e^x = x` doesn't have an analytical solution, just a numerical one.

Generally, the best method of solving these is Newton's method, numerically approximating the solution.

In this case, it is pretty easy for a calculator to find that there is a solution around -1.2 and one around -0.26.