# Exponential and Logarithmic Functions

by
**wallywill**

Last updated 8 years ago

** Discipline: **

Math ** Subject: **

Pre-Calculus

Exponential & Logarithmic Functions

D: (-∞,∞) R: (0,∞)

D: (0,∞) R: (-∞, ∞)

f(x) =a^x

f(x)=log(base"b")x

A function where the constant, "a", is raised to the power of variable "x".

The logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number.

The number "e" ≈ 2.718281828459(irrational # like π)y=e^x ≈ y=2.718^x

A log that isn't followed by a base number is a common log. Common log's have a base of 10.

Natural logs have a base of "e".x=e^ln(x) can be converted to x=ln(e^x).

○ ln100=2

○ log37=1.568

○ln4=1.836

○ln1=0

The exponential equation a^y=x can be converted to log(base"a")=y.

INTEREST

Exponential and logarithmic functions can be used to calculate both compound and continous interest.

COMPOUND INTEREST - A(t)=P[1+(r/t)]^nt

CONTINUOUS INTEREST - A(t)=Pe^rt

A(t) - Amount of time "t"P - Principle amountr - Interest raten - Times the interest is compounded a yeart - Time in years

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