Evaluate the expression ln1 and lne^7

[theevilp0ptart]

Evaluate the expressions with using a calculator

ln1
I believe this one equals 0 because of the 1.

lne^7
I think this one equals 7.

Am I right? How would I show why?

 

[pka]

You are correct.
\(\displaystyle \ln(1)=0\)
\(\displaystyle \ln(e)=1\)
\(\displaystyle \ln(e^a)=a\)

 

[Loren]

I am assuming that you are taking "ln" to mean the logarithm to base e.

If e[sup:a81duwqa]x[/sup:a81duwqa] = a, then ln[sub:a81duwqa]e[/sub:a81duwqa]a = x and visa versa by definition.

ln[sub:a81duwqa]e[/sub:a81duwqa]1 = x >>> e[sup:a81duwqa]x[/sup:a81duwqa] = 1. ... x=0 by definition.

You are correct on the first one. Does this help on the second one?