Glossary for Lesson 33: Solving Exponential and Logarithmic Equations

Product property

The product property of logarithms can be stated as the following:
\log_aAB=\log_aA+\log_bB

Quotient property

The quotient property of logarithms can be stated as the following:
\log_a\frac{A}{B}=\log_aA-\log_aB

Power Property

The power property of logarithms can be stated as the following:
\log_aA^n=n\log_aA

Change of Base Formula

In order to change the base of a logarithmic expression without changing its value, we can use the change of base formula:
\log_ax=\frac{\log_bx}{\log_ba}

One-to-One Properties of Exponents and Logs

a^x=a^y if and only if x=y
\log_ax=\log_ay if and only if x=y

Inverse Properties of Exponents and Logs

a^{\log_ax}=x
\log_aa^x=x