Step-by-step Solution

Evaluate the limit of $\frac{5x}{\ln\left(1-3x\right)}$ as $x$ approaches 0

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Step-by-step explanation

Problem to solve:

$\lim_{x\to0}\left(\frac{5x}{\ln\left(1-3x\right)}\right)$

Learn how to solve limits problems step by step online.

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(5x\right)}{\frac{d}{dx}\left(\ln\left(1-3x\right)\right)}\right)$

Unlock this full step-by-step solution!

Learn how to solve limits problems step by step online. Evaluate the limit of (5x)/(ln(1-3*x) as x approaches 0. If we try to evaluate the limit directly, it results in indeterminate form. Then we need to apply L'Hôpital's rule. The derivative of the linear function times a constant, is equal to the constant. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The derivative of a sum of two functions is the sum of the derivatives of each function.

Final Answer

$-\frac{5}{3}$$\,\,\left(\approx -1.6666666666666667\right)$
$\lim_{x\to0}\left(\frac{5x}{\ln\left(1-3x\right)}\right)$

Main topic:

Limits

Related formulas:

7. See formulas

Time to solve it:

~ 0.07 s (SnapXam)