Final answer to the problem
$\frac{1}{\ln\left(5\right)}$
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Step-by-step Solution
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- Solve using L'Hôpital's rule
- Solve without using l'Hôpital
- Solve using limit properties
- Solve using direct substitution
- Solve the limit using factorization
- Solve the limit using rationalization
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
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1
The limit of the product of two functions is equal to the product of the limits of each function
$\lim_{x\to0}\left(5^x\right)\lim_{x\to0}\left(\frac{x}{5^x-1}\right)$
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$\lim_{x\to0}\left(5^x\right)\lim_{x\to0}\left(\frac{x}{5^x-1}\right)$
Learn how to solve problems step by step online. Find the limit of (x5^x)/(5^x-1) as x approaches 0. The limit of the product of two functions is equal to the product of the limits of each function. Evaluate the limit \lim_{x\to0}\left(5^x\right) by replacing all occurrences of x by 0. Any expression multiplied by 1 is equal to itself. If we directly evaluate the limit \lim_{x\to0}\left(\frac{x}{5^x-1}\right) as x tends to 0, we can see that it gives us an indeterminate form.
Final answer to the problem
$\frac{1}{\ln\left(5\right)}$
