A logarithm is a mathematical function that represents the relationship between a base and its exponent. It essentially tells you how many times the base must be multiplied by itself to equal a given number.
Logarithms are useful because they allow us to solve exponential equations and perform calculations involving very large or very small numbers. They also help us compare values that differ by orders of magnitude.
A log, or logarithm, is a function with a base of 10, while ln, or natural logarithm, is a function with a base of e (approximately 2.718). In other words, log is base 10 and ln is base e.
To solve a logarithmic equation, you can use the properties of logarithms to rewrite the equation in a simpler form and then solve for the variable. Alternatively, you can convert the logarithmic equation into an exponential equation and solve for the variable.
Logarithms are commonly used in science to measure the intensity of earthquakes, sound, and light, as well as to represent the pH scale for acids and bases. They are also used in biology to measure the loudness of sounds and the brightness of stars.