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Exercise

$\lim_{x\to+a}\left(\frac{ln\left(x-a\right)}{ln\left(e^x-e^a\right)}\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to+a}\left(\frac{\ln\left(x-a\right)}{\ln\left(e^x-e^a\right)}\right)$ by replacing all occurrences of $x$ by $+a$

$\frac{\ln\left(+a-a\right)}{\ln\left(e^{+a}-e^a\right)}$

Final answer to the exercise

$\frac{\ln\left(+a-a\right)}{\ln\left(e^{+a}-e^a\right)}$

Try other ways to solve this exercise

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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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Main Topic: Special Products

Special products is the multiplication of algebraic expressions that follow certain rules and patterns, so you can predict the result without necessarily doing the multiplication.

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