It looks like you have two equations here, but there might be some formatting issues. Let's try to clarify and solve them one by one.

### Equation 1: $2^x + 1 - 2 = 32$

First, simplify the equation:
$$2^x + 1 - 2 = 32$$

Combine like terms:
$$2^x - 1 = 32$$

Add 1 to both sides to isolate $2^x$:
$$2^x = 33$$

Now, solve for $x$:
$$x = \log_2(33)$$

This is the exact solution. If you need a numerical approximation, you can use a calculator:
$$x \approx 5.044$$

### Equation 2: $mũ x + 1 - 2 = 32$

It seems like there might be a typo here. If you meant $3^x + 1 - 2 = 32$, let's solve that:

First, simplify the equation:
$$3^x + 1 - 2 = 32$$

Combine like terms:
$$3^x - 1 = 32$$

Add 1 to both sides to isolate $3^x$:
$$3^x = 33$$

Now, solve for $x$:
$$x = \log_3(33)$$

This is the exact solution. If you need a numerical approximation, you can use a calculator:
$$x \approx 3.178$$

If you meant something else by "mũ x + 1 - 2 = 32," please clarify, and I'll be happy to help further.