Variables as arguments of exponential function make equation not linear? A Linear Algebra textbook I'm reading says the equation $$e^{x+y+z}=1$$ is not linear because x, y, and z are arguments of the exponential function. But I believe taking the natural log of both sides makes this $$x+y+z=\ln(1)$$ which is linear. Why isn't the first equation linear?
An equation in $x,y,z$ is linear  if it has the form $$ax+by+cz=d.$$Period. The equation $e^{x+y+z}=1$ is not of that form, so it's not linear.

It's equivalent to the linear equation $x+y+z=0$, but it's not the same equation.
An equation in $x,y,z$ is linear  if it has the form $$ax+by+cz=d.$$Period. The equation $e^{x+y+z}=1$ is not of that form, so it's not linear.

It's equivalent to the linear equation $x+y+z=0$, but it's not the same equation.