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balu736 [363]
2 years ago
9

Find the exact value of the logarithm without using a calculator.

Mathematics
2 answers:
xz_007 [3.2K]2 years ago
6 0

Answer:

\frac{1}{11}

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

ln(x) =log_{e}(x)

ln(\sqrt[11]{e} ) = log_{e}(\sqrt[11]{e} )

We can take this one step further if we realize that we can rewrite the square root as a simple power to a fraction!

log_{e}(e^{\frac{1}{11} } )

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.

e^{x} = e^{\frac{1}{11} }

Well x has to be 1/11 in that case. And that ends up being our final answer.

log_{e}(e^{\frac{1}{11} } ) = \frac{1}{11}

denis-greek [22]2 years ago
5 0

Answer:

1/11

Step-by-step explanation:

We are asked to find the natural log of

\sqrt[11]{e}

Convert to fractional exponent

ln(e {}^{ \frac{1}{11} } )

Apply Log of Power rule

\frac{1}{11}  ln(e)

Natural log of e is 1 so

\frac{1}{11}  \times 1 =  \frac{1}{11}

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