What do these mathematical relationship mean
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What do these mathematical relationship mean

[From: ] [author: ] [Date: 11-05-27] [Hit: ]
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),basically the relationship is the same equation, just with different dependent variables.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.......
z=log w if w=e^z

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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

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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

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z = ln w if w = e^z

z = log w if w = 10^z

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z=log w is only valid for values of w=e^z
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