We are asked to solve two equations: (a) $ln(x) = 2$ (b) $e^{x+7} = 4$

1. Problem Description

We are asked to solve two equations:

(a) $ln(x) = 2$

(b) $e^{x+7} = 4$

2. Solution Steps

(a) To solve the equation $ln(x) = 2$, we can exponentiate both sides with base $e$.

$e^{ln(x)} = e^2$

Since $e^{ln(x)} = x$, we have:

$x = e^2$

(b) To solve the equation $e^{x+7} = 4$, we can take the natural logarithm of both sides.

$ln(e^{x+7}) = ln(4)$

Since $ln(e^{x+7}) = x+7$, we have:

$x+7 = ln(4)$

Subtracting 7 from both sides, we get:

$x = ln(4) - 7$

3. Final Answer

(a) $x = e^2$

(b) $x = ln(4) - 7$