Evaluate g(x) = ln(x), for x = e^3

[jwpaine]

Evaluate the function at the indicated value of x without using a calculator.
g(x) = ln(x)          x = e^3

Ok.. so ln(x) is the natural logarithm: so ln(x) = log(e)^x

So would g(x) = ln(x), for x = e^3 be ln(e^3) = log(e)^(e^3) ?

I'm not sure what to do with this. The answer should be 3.


Thanks for the help.

 

[Gene]

The clue is "without using a calculator" so stick with
g(x) = ln(e^3)
Do you know how to raise something to a power using lns? Like ln(x^5) = 5*ln(x)
Do you know what ln(e) equals?
Think abbout those two things.

 

[jwpaine]

Thank you for your help.
I understand now.

Because natural base e is the inverse of the natural logarithm,
the identity ln(e^x) = x

so, ln(e) = 1

There for ln(e^3) = 3ln(e) = 3(1) = 3