1. The problem states that $\ln(a) = \ln(b)$ and asks to find the relationship between $a$ and $b$. 2. Recall the property of logarithms: if $\ln(x) = \ln(y)$, then $x = y$ for $x, y > 0$ because the natural logarithm function is one-to-one. 3. Applying this property directly, since $\ln(a) = \ln(b)$, it follows that: $$a = b$$ 4. This means the values inside the logarithms must be equal for their logarithms to be equal. 5. Important note: this holds only if $a > 0$ and $b > 0$ because the natural logarithm is defined only for positive real numbers. Final answer: $$a = b$$