What are logarithmic functions and how do they work?

What are logarithmic functions and how do they work?

Logarithmic functions are the inverses of exponential functions. They help us solve equations where the variable is an exponent.

Can you give me an example of a logarithmic function?

Sure! The function f(x) = log_b(x) is a logarithmic function, where b is the base. For example, log_10(100) = 2 because 10^2 = 100.

What are some real-world applications of logarithmic functions?

Logarithmic functions are used in various fields, such as measuring sound intensity in decibels, pH in chemistry, and in financial models.

How do you convert between exponential and logarithmic forms?

To convert from exponential to logarithmic form, you can use the formula: if b^y = x, then log_b(x) = y.

What is the natural logarithm and how is it different from common logarithm?

The natural logarithm, denoted as ln(x), uses the base e (approximately 2.718), while the common logarithm uses base 10.