Simplify e^ x2, 4 + 25, and solve 3 x + (x)/(2) = 4.

$$e^{\ln x^2} = x^2$$

The expression is defined for $x \neq 0$.

The simplified expression is $\boxed{x^2}$.

1b) Simplify $\log 4 + \log 25$.

Assuming base 10 for $\log$.

$$= 2$$

The simplified expression is $\boxed{2}$.

2a) Solve for $x$ in the equation $3 \log x + \log \frac{x}{2} = 4$.

$$\log \left( x^3 \cdot \frac{x}{2} \right) = 4$$ $$\log \left( \frac{x^4}{2} \right) = 4$$

Assuming base 10 for $\log$.

$$\frac{x^4}{2} = 10^4$$

$$\frac{x^4}{2} = 10000$$ $$x^4 = 2 \times 10000$$ $$x^4 = 20000$$

$$x = \sqrt[4]{20000}$$ $$x = \sqrt[4]{2 \times 10^4}$$ $$x = 10 \sqrt[4]{2}$$

For the logarithms to be defined, $x > 0$. The solution $10 \sqrt[4]{2