Final answer to the problem
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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Change the logarithm to base $e$ applying the change of base formula for logarithms: $\log_b(a)=\frac{\log_x(a)}{\log_x(b)}$
Learn how to solve limits to infinity problems step by step online.
$\lim_{x\to\infty }\left(\frac{\frac{\ln\left(x^2\right)}{\ln\left(3\right)}}{e^x}\right)$
Learn how to solve limits to infinity problems step by step online. Find the limit of log3(x^2)/(e^x) as x approaches infinity. Change the logarithm to base e applying the change of base formula for logarithms: \log_b(a)=\frac{\log_x(a)}{\log_x(b)}. Divide fractions \frac{\frac{\ln\left(x^2\right)}{\ln\left(3\right)}}{e^x} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. If we directly evaluate the limit \lim_{x\to\infty }\left(\frac{\ln\left(x^2\right)}{\ln\left(3\right)e^x}\right) as x tends to \infty , we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately.
