Practice Natural Logarithm in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The logarithm with base e \approx 2.71828: \ln x = \log_e x. It is the inverse function of e^x.
If e^x asks 'what do I get after growing continuously for time x?', then \ln x asks 'how long do I need to grow continuously to reach x?' The natural log measures time in the world of continuous growth.
Example 1
easyEvaluate \ln(e^5).
Example 2
mediumSimplify \ln(x^3) - 2\ln(x) + \ln(e).
Example 3
mediumSolve \ln(2x + 1) = 3 for x.
Example 4
hardFind the derivative of f(x) = \ln(x^2 + 1) and determine where f is increasing.