Solving Exponential and Logarithmic Equations

Two basic strategies:

-one-to-one properties

if and only if  x=y

if and only if x=y

-inverse properties

= x

Strategies:

1- Rewrite the given equation in a form to use the one-to-one properties of exponential or logarithmic functions.

2- Rewrite an exponential equation in logarithmic form and apply the inverse property of logarithmic functions.

3- Rewrite a logarithmic equation in exponential form and apply the inverse property of exponential functions.

Example-

=5

=

=

2x=

x=

x= 0.112



Continuous Compounding-

Change of Base Formula-