I. Introduction 
What you should learn
How to solve simple
exponential and
logarithmic equations 
State the OnetoOne Property for
exponential equations. a^{x} = a^{y} if and
only if x = y
State the OnetoOne Property for logarithmic
equations.
if and only
if x = y
State the Inverse Properties for exponential
equations and for
logarithmic equations.
Describe how the OnetoOne Properties and the
Inverse
Properties can be used to solve exponential and logarithmic
equations.
· Rewrite the given equation in a form that
allows the use
of the OnetoOne Properties of exponential or
logarithmic functions to solve the equation.
· Rewrite an exponential equation in logarithmic form and
apply the Inverse Property of logarithmic functions to
solve the equation.
· Rewrite a logarithmic equation in exponential form and
apply the Inverse Property of exponential functions to
solve the equation.
Example 1:
(a) Solve
for x.
(b) Solve 5^{x} = 0.04 for x.
(a) x = 2 (b) x =  2 

II. Solving Exponential Equations 
What you should learn
How to solve more
complicated exponential
equations 
Describe how to solve the exponential
equation 10^{x} = 90
algebraically.Take the common logarithm
of each side of the equation and
then use the Inverse Property to obtain: x = log 90. Then use a
calculator to approximate the solution by evaluating log 90 ≈
1.954.
Example 2: Solve e ^{x2}  7 = 59 for x.
Round to three decimal
places.
x ≈ 6.190 

III. Solving Logarithmic Equations 
What you should learn
How to solve more
complicated logarithmic
equations 
Describe how to solve the logarithmic
equation
algebraically.
Use the OnetoOne Property for logarithms to write the
arguments of each logarithm as equal: (4x  7) = (8  x). Then
solve this resulting linear equation by adding 7 to each side,
adding x to each side, and then finally dividing both sides by 5.
The solution is x = 3.
Example 3:
Solve 4 ln 5x = 28 for x. Round to three decimal
places.
x ≈ 219.327 

IV. Approximating Solutions 
What you should learn
How to approximate the
solutions of exponential
or logarithmic equations
with a graphing utility 
Describe at least two different
methods that can be used to
approximate the solutions of an exponential or logarithmic
equation using a graphing utility.Graph the lefthand side and the righthand side of the equation
in the same viewing window; then use the intersect feature or the
zoom and trace features of the graphing utility to find the points
of intersection. OR rewrite the equation so that all terms on the
left side are equal to 0. Then use a graphing utility to graph the
left side of the equation. Use the zero or root feature or the zoom
and trace features to approximate the solutions of the equation. 

V. Applications of Solving
Exponential and Logarithmic
Equations 
What you should learn
How to use exponential
and logarithmic equations
to model and solve reallife
problems 
Example 4:
Use the formula for
continuous compounding,
, to find how long it will take $1500 to
triple in value if it is invested at 12% interest,
compounded continuously.
t ≈ 9.155 years 
