Logarithms

Properties of Exponents

1. negative exponents can be changed to positive exponents by moving them to the numerator or denominator 2. multiply = add exponents

strategies for solving exponential and logarithmic equations

1. rewrite the original equation in a form that allows the use of 1 to 1 property 2. rewrite an exponential equation in logarithmic form and apply the inverse property of logarithms functions 3. rewrite a logarithmic equations in exponential form and apply the inverse property of exponential functions

logarithmic equation

An equation that contains one or more logarithms

Change-of-Base Formula for Logarithms

log b^a = log a/log b = ln a /ln b

natural logarithmic function

the inverse function of f(x)=e^x

Properties of Logarithms

-log(b) xy = log(b) x + log(b) y -log(b) x/y = log(b) x - log(b) y -log(b) x^y = ylog(b) x

One-to-one property

If a^x=a^y, then x=y

Inverse property of logarithms

alog ax = x log a a^x=x