Question: top-left: $e^{\frac{x^3}{4}} = 2$.
1. **State the problem:** Solve the equation $$e^{\frac{x^3}{4}} = 2$$ for $x$.
2. **Recall the formula and rules:** The natural exponential function $e^y$ is one-to-one, so if $e^A = e^B$, then $A = B$. Also, to solve for $x$, we can take the natural logarithm $\ln$ on both sides to undo the exponential.
3. **Apply the natural logarithm:**
$$\ln\left(e^{\frac{x^3}{4}}\right) = \ln(2)$$
Using the property $\ln(e^y) = y$, we get:
$$\frac{x^3}{4} = \ln(2)$$
4. **Isolate $x^3$:**
Multiply both sides by 4:
$$\cancel{4} \times \frac{x^3}{\cancel{4}} = 4 \times \ln(2)$$
$$x^3 = 4 \ln(2)$$
5. **Solve for $x$:**
Take the cube root of both sides:
$$x = \sqrt[3]{4 \ln(2)}$$
6. **Final answer:**
$$\boxed{x = \sqrt[3]{4 \ln(2)}}$$
This is the exact solution for $x$ in terms of natural logarithm.