Review
1) Suppose you buy a car for $23,000 that depreciates at a rate of 8.5% per year. How much will you the car be worth after 5 years?
Find the annual percent increase or decrease each function models.
2) y = 15000(.95)x
3) y = 3(1.075)x
Key Concepts for Sect. 8.3
*Remember that an inverse is the mirror image (reflected over y = x) of a function.
*A logarithmic function is the inverse of an exponential function.
For example,
y = 3x and y = log3 x are inverses of each other.
*log10 x log x (common logarithm)
*loge x ln x (natural logarithm)
*Use your graphing calculator to graph the functions below. Are they inverses of each other?
y = 10x y = log x
Guided Practice for Sect. 8.3
Ex 1: Rewrite each equation in exponential form.
a)
log2 32 = 5
b)
log5 1 = 0
c)
log4 64 = 3
Guided Practice for Sect. 8.3
Ex 2: Write each equation in logarithmic form.
a) 36 = 62
b) 125 = 53
c) 81 = 34
d) 3 = 91/2
e) 1/8 = 2­3
Guided Practice for Sect. 8.3
Ex 3: Evaluate each expression without using a calculator.
a)
log2 64
b)
log3 81
c)
log25 5
d)
log1/2 8
Key Concepts for Sect. 8.3
Find the inverse of each function.
y = log9 x
a)
b)
y = log x
c)
y = ln 5x
d)
y = ln (x ­ 4)