Logarithmic Functions

Notes:

Terms

Definition of Logarithm: A logarithm can be defined as an exponent.

  • loga(b) = c means the same as ac = b

    • “loga(b) is the power to which we raise ‘a’ to get ‘b’.“

Natural Logarithms: These are logarithms with base ‘e’ (Euler’s Number).

  • loge(x) is abbreviated ln(x).

    • “ln(x) is the power to which we raise ‘e’ (Euler’s number) to get ‘x’.”

Common Logarithms: These are logarithms with base 10.

  • log10(x) is abbreviated log(x).

    • “log(x) is the power to which we raise 10 to get x”

Inverse Functions: “Whatever one of the function does, the other one undoes.”

  • Example: f(x)=log2x and g(x)=2x are Inverse Functions.

  • f(g(x)) = alogaX = X

  • g(f(x)) = logaaX = X

Extra

“0 cannot go into Logarithms!”

Richter Scale: Intensity of an earthquake is measured on the Richter Scale.

The formula: R = log(I/I0), where I0 is the intensity of the “zero quake”, the very tiny earthquake which all others are measured, and I is the intensity of the quake being measured.