Learn how to solve one-variable linear inequalities problems step by step online. Find the limit of (x^(100log(x)))/(2^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)}. Evaluate the limit \lim_{x\to\infty }\left(\frac{x^{\frac{100\ln\left(x\right)}{\ln\left(10\right)}}}{2^x}\right) by replacing all occurrences of x by \infty . Apply a property of infinity: k^{\infty}=\infty if k>1. In this case k has the value 2. The natural log of infinity is equal to infinity, \lim_{x\to\infty}\ln(x)=\infty.

Find the limit of (x^(100log(x)))/(2^x) as x approaches infinity