Evaluate natural logarithms

Learning Objectives Define the natural logarithm and its base, the number 'e'. Evaluate basic natural logarithmic expressions without a calculator, such as ln(1) and ln(e). Apply the inverse property to simplify and evaluate expressions like ln(e^x). Use a scientific calculator to find the approximate decimal value of natural logarithms. Simplify expressions involving natural logarithms using properties before evaluating. Distinguish between an exact answer and a decimal approximation for a natural logarithm. How does a bank calculate interest that is compounded every single second? The answer lies in a special number and its logarithm! 📈 This tutorial will introduce you to the natural logarithm, often written as 'ln(x)'. You will learn about its specia...

TermDefinitionExample The Number 'e' (Euler's Number)An irrational and transcendental constant, approximately equal to 2.71828. It is the base of the natural logarithm and arises naturally in studies of compound interest, calculus, and other areas involving continuous growth.The value of e is approximately 2.718. It's like pi (π), but for growth. Natural LogarithmA logarithm with a base of 'e'. It is written as ln(x), which is shorthand for log_e(x). The natural logarithm of a number 'x' is the power to which 'e' must be raised to equal 'x'.ln(7.389) ≈ 2, because e^2 ≈ 7.389. Argument of a LogarithmThe quantity or number that you are taking the logarithm of. The argument must always be a positive number.In the expression ln(5x),...

Logarithm of 1 ln(1) = 0 The natural logarithm of 1 is always 0. This is because e^0 = 1. Logarithm of the Base ln(e) = 1 The natural logarithm of e is always 1. This is because e^1 = e. Inverse Property 1 ln(e^x) = x The natural logarithm of 'e' raised to a power 'x' is simply 'x'. The logarithm and the exponential function cancel each other out. Inverse Property 2 e^(ln x) = x Raising 'e' to the power of the natural logarithm of 'x' results in 'x'. This is the other form of the inverse property, valid for x > 0.