8.5 Exponential and Logarithmic Equations
The best and safest thing is to keep a balance in your
life, acknowledge the great powers around us and in us.
We will use logarithms to undo exponents.
We will use this property of logarithms:
logb M  x logb M
x
Exponential Equations
Take the common logarithm of both sides
3 4
x
3
x4
 101
26
2x
 23
Exponential Equations
By graphing…
6  1500
2x
1. Graph:
2. Find point of intersection (2nd -> Calc -> Intersect)
calc
Logarithmic Equations
Change of Base Formula:
Ex: Evaluate log 3 15
log M
log b M 
log b
Logarithmic Equations
When x is in the argument of the logarithm and nothing can be
moved around…convert equation to an exponential function.
log 3 x  1  5
log 7  2 x   1
Logarithmic Equations
When there are multiple logarithms…
Write as a single logarithm, THEN put in exponential form!
2 log x  log 3  2
log 6  log 3x  2
3 log x  log 2  5
8.5 Exponential and Logarithmic Equations
HW: 1-13 odd, 25-47 odd
The best and safest thing is to keep a balance in your
life, acknowledge the great powers around us and in us.