Final answer:
Natural logarithms are used in real-life for compound interest calculations and population growth modeling. The natural logarithm of a number is the exponent to which the base e must be raised. Calculations with natural logarithms follow specific operation rules such as summing logarithms when multiplying numbers.
Step-by-step explanation:
The natural logarithm of a number (ln) is the power to which e (approximately 2.7182818) must be raised to equal the number. For instance, the natural logarithm of 10 is approximately 2.303, because e to the power of 2.303 equals 10.
Real-life applications of natural logarithms include:
- Compound interest calculations, where the natural logarithm helps in solving the time needed for an investment to grow to a certain amount at a continuous compound rate.
- Population growth modeling, where natural logarithms are used to transform exponential growth equations into linear ones for ease of analysis and understanding.
To perform calculations involving natural logarithms, you can use the ln button on your calculator. To reverse the process and get the number from its natural logarithm, you would calculate ex where x is the natural logarithm of the number.
Operation rules for logarithms indicate, for example, that the logarithm of a product of two numbers is the sum of the logarithms of those two numbers (ln xy = ln x + ln y).