October 06, 2014
3.3 Solving Exponential Equations
Objective: Solve exponential equations using the Power Property of equality
So far we have been simplifying expressions containing exponents, now we will look at equations
with variable exponents.
Exponential Equations - An equation where variables occur as exponents
Ex: 2x = 8
How
these
olve
s
e
do w
?
2x = 8
1) Rewrite in base 2
2) Use Power Property of Equality
Power Property of Equality
For any real number b > 0 and b ≠ 1, bx = by if and only if x = y.
Example: If 5x = 54
Let's try some...
Ex1: a) 11x = 121
b) 6x = 216
c) 5x = 625
Ex2: a) 25x-1 = 5
b) 122x+3 = 144
c) 4x-2 = 1
32
1
( )
n-49
Ex3: The frequency f in hertz of the nth key on a piano is f = 440 212 .
http://www.sengpielaudio.com/calculator-notenames.htm
Middle C, n = 40
Concert A, n = 49
a) What is the frequency of Concert A?
b) Which note has a frequency of 220 Hz?
October 06, 2014
Ex4: Application
Suppose you go on a walk where you choose the direction of each step at random. The path of a
molecule in a liquid or a gas, the path of a foraging animal, and a fluctuating stock price are all
modeled as random walks. The number of possible random walks w of n steps where you choose one of
d directions at each step is w = dn.
a) How many steps have been taken in a 2-direction random walk if there are 4096 possible walks?
b) How many steps have been taken in a 4-direction random walk if there are 65,536 possible walks?
c) If a walk of 7 steps has 2187 possible walks, how many directions could be taken at each step?