evaluate the logarithmic equation

ln e ^ 2

Question

evaluate the logarithmic equation 

ln e ^ 2

lgbasallote · Answer

use power rule..you know how to do that right?

anonymous · Answer

$$\log_b(b^x)=x$$

anonymous · Answer

?

anonymous · Answer

and $$\log_e(z)=\ln(z)$$

lgbasallote · Answer

power rule still works @satellite73 :P

lgbasallote · Answer

and $\ln e = 1$

anonymous · Answer

you are composing a function with its inverse
$$f(x)=e^x,f^{-1}(x)=\ln(x)$$ so 
$$\ln(e^x)=x$$ and also $$e^{\ln(x)}=x$$

anonymous · Answer

isn't it 2e^2

anonymous · Answer

no, it is 2

anonymous · Answer

i put that the answer was 1 on my test and i got it wrong...

lgbasallote · Answer

$\ln e^{x} = x\ln e = x$

my way :P haha

anonymous · Answer

but the exponent doesn't change...according to the rules.....at least that's what I remember....but maybe I'm wrong....

anonymous · Answer

$\ln(e^x)=x$ and so $\ln(e^2)=2$ just like $\log_5(5^2)=2$

anonymous · Answer

could the answer just be e?

anonymous · Answer

so its 2?

anonymous · Answer

yes it is 2

lgbasallote · Answer

yes 2

anonymous · Answer

ok so how did you find that... cause im stupid

anonymous · Answer

you are asking the following question: what number would you raise e to in order to get $e^2$ and the answer is clearly 2

anonymous · Answer

as i wrote above, it is always the case that $\log_b(b^x)=x$

lgbasallote · Answer

there are 2 ways... satellite's way is the logarithmic propert $\ln e^x = x$ my way is $\ln e^x = x \ln e = x$

anonymous · Answer

it is a tautology, like asking who is buried in grants tomb

anonymous · Answer

$\log_{10}(10^6)=6$ etc