Answer:
1/11
Step-by-step explanation:
We are asked to find the natural log of
[tex] \sqrt[11]{e} [/tex]
Convert to fractional exponent
[tex] ln(e {}^{ \frac{1}{11} } ) [/tex]
Apply Log of Power rule
[tex] \frac{1}{11} ln(e) [/tex]
Natural log of e is 1 so
[tex] \frac{1}{11} \times 1 = \frac{1}{11} [/tex]
Answer:
[tex]\frac{1}{11}[/tex]
Step-by-step explanation:
First, remember that the ln function is just a log function with a base of e. Here's how it looks
[tex]ln(x) =log_{e}(x)[/tex]
[tex]ln(\sqrt[11]{e} ) = log_{e}(\sqrt[11]{e} )[/tex]
We can take this one step further if we realize that we can rewrite the square root as a simple power to a fraction!
[tex]log_{e}(e^{\frac{1}{11} } )[/tex]
Solving the equation above is really simple. All that function is really saying is can we raise e to some number, where the result would be e^(1/11)? In other words find x.
[tex]e^{x} = e^{\frac{1}{11} }[/tex]
Well x has to be 1/11 in that case. And that ends up being our final answer.
[tex]log_{e}(e^{\frac{1}{11} } ) = \frac{1}{11}[/tex]
