Simplify the expression. Assume all variables represent positive real numbers. $\ln \left( e ^ { - 9 x ^ { 2 } + 19 x } \right)$
A) $- 9 x ^ { 2 } + 19 x$
B) $19 x \cdot \ln \left( e ^ { - 9 x ^ { 2 } } \right)$
C) $1 ^ { - 9 x ^ { 2 } + 19 x }$
D) $e ^ { - 9 x ^ { 2 } + 19 x }$

Question

Quizplus · Accepted Answer

The logarithm function $\ln$ is the inverse of the exponential function $e^x$. Therefore, $\ln(e^y) = y$ for any $y$, simplifying the given expression to $-9x^2 + 19x$.

Simplify the Expression ln⁡(e−9x2+19x)\ln \left( e ^ { - 9 x ^ { 2 } + 19 x } \right)ln(e−9x2+19x)

Simplify the Expression $\ln \left( e ^ { - 9 x ^ { 2 } + 19 x } \right)$