The equation e^(-1) = c can be rewritten in logarithmic form as ln(e^(-1)) = ln(c), which simplifies to -1 = ln(c). The discussion highlights a misunderstanding of logarithms, questioning the source of the logarithm problems being posed. It emphasizes the equivalence between exponential and logarithmic forms, stating that if y = a^x, then log_a(y) = x. Understanding these concepts is crucial for solving logarithmic equations effectively. The conversation underscores the importance of grasping the fundamentals of logarithms for accurate problem-solving.