Learn how to solve problems step by step online. Find the limit of log(1+x)/(cos(3x)-e^(-x)) as x approaches 0. 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(1+x\right)}{\ln\left(10\right)}}{\cos\left(3x\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}. Evaluate the limit \lim_{x\to0}\left(\frac{\ln\left(1+x\right)}{\ln\left(10\right)\left(\cos\left(3x\right)-e^{-x}\right)}\right) by replacing all occurrences of x by 0. Add the values 1 and 0.

Find the limit of log(1+x)/(cos(3x)-e^(-x)) as x approaches 0