# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\lim_{x\to0}\left(\left(1-e^x\right)^{\frac{1}{\ln\left(x\right)}}\right)$

Learn how to solve limits of exponential functions problems step by step online.

$y=\lim_{x\to0}\left(\left(1-e^x\right)^{\frac{1}{\ln\left(x\right)}}\right)$

Learn how to solve limits of exponential functions problems step by step online. Evaluate the limit (x)->(0)lim((1-e^x)^(1/(ln(x))). Because this limit results in a indeterminate form, and it is not possible to apply L'Hôpital's rule, we have to do something special in order to be able to solve it. Let's say y is equal to the original limit. Now, let's apply natural logarithm to both sides of the equality. This is necessary in order to simplify the exponential function that is inside the limit. The logarithm of a limit is equal to the limit of the logarithm. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x).

$e$$\,\,\left(\approx 2.718281828459045\right)$
$\lim_{x\to0}\left(\left(1-e^x\right)^{\frac{1}{\ln\left(x\right)}}\right)$