z=log w if w=e^z
-
i assume that you mean the natural log. based off that assumption:
first, this is just a simple substitution.
lets take z = log(w) and plug w = e^z into the first equation.
z = log(e^z). now we just rewrite the equation using logarithm rules.
z = z*log(e) since the base of the natural logarithm is e, the log(e), "cancels" out leaving you with
z = z
basically the relationship is the same equation, just with different dependent variables.
in the first equation z is the dependent variable while w is independent
in the second equation w is the dependent variable while z is indepent
first, this is just a simple substitution.
lets take z = log(w) and plug w = e^z into the first equation.
z = log(e^z). now we just rewrite the equation using logarithm rules.
z = z*log(e) since the base of the natural logarithm is e, the log(e), "cancels" out leaving you with
z = z
basically the relationship is the same equation, just with different dependent variables.
in the first equation z is the dependent variable while w is independent
in the second equation w is the dependent variable while z is indepent
-
You can think of Log and e "inverse" so they "cancel" each other out. When you substitute w in, you get:
z=log(e^z) and since log and e "cancel" it is true that z=z. But you can only do this when "z" is in the exponent of e
z=log(e^z) and since log and e "cancel" it is true that z=z. But you can only do this when "z" is in the exponent of e
-
z = ln w if w = e^z
z = log w if w = 10^z
z = log w if w = 10^z
-
z=log w is only valid for values of w=e^z