Logarithms and their basic properties A logarithm is a function that undoes another mathematical function, like taking the square root. We call this function...
A logarithm is a function that undoes another mathematical function, like taking the square root. We call this function the logarithm.
Basic Properties of Logarithms:
Log(a^b) = b - This means that if we take the logarithm of a number raised to a power, we get the exponent.
log(a) - log(b) = log(a/b) - This tells us that we can remove the same value from the numerator and denominator of a logarithm, as they are essentially the same number.
log(a) + log(b) = log(ab) - This tells us that we can add the logarithms of two numbers together to find the logarithm of their product.
log(a) - log(b) = log(a/b) - This tells us that we can remove the same value from the numerator and denominator of a logarithm, as they are essentially the same number.
Examples:
log(9) = 2 - This means that 9 is 2 raised to the power of 2.
log(4) = 2 - This means that 4 is 2 raised to the power of 2.
log(16) = 4 - This means that 16 is 2 raised to the power of 4.
log(0.25) = 0 - This means that 0.25 is 1/4 raised to the power of 0.
These properties allow us to perform various operations with logarithms, such as finding the inverse of a function, solving inequalities, and simplifying expressions