To solve the equation:

$31 = 2^x - 3$

we can isolate $2^x$ and solve for $x$:

1. Add 3 to both sides to isolate the term with $x$:

   $31 + 3 = 2^x$

   $34 = 2^x$

2. Rewrite in logarithmic form to solve for $x$:

   $x = \log_2 34$

3. Now, we can approximate $x$ using the change of base formula:

   $x = \frac{\log 34}{\log 2} \approx 5.09$

So, the solution is approximately:

$x \approx 5.09$

Would you like a more detailed explanation of the steps or further assistance?

Here are some related questions to consider:

1. How do logarithmic functions help solve exponential equations?
2. What is the change of base formula, and how is it applied?
3. How can you solve exponential equations with different bases?
4. What role do natural logarithms play in solving exponential functions?
5. How does rounding affect the accuracy of solutions in exponential equations?

Tip: Always verify exponential equations by substituting the solution back into the original equation.