Learn how to solve limits by l'hôpital's rule problems step by step online. Find the limit of loge(x/6)/(x^3-216) as x approaches 6. 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(\frac{x}{6}\right)}{\ln\left(e\right)}}{x^3-216} 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}. Calculating the natural logarithm of e. If we directly evaluate the limit \lim_{x\to6}\left(\frac{\ln\left(\frac{x}{6}\right)}{x^3-216}\right) as x tends to 6, we can see that it gives us an indeterminate form.

Find the limit of loge(x/6)/(x^3-216) as x approaches 6