7.4 Day 1.notebook
January 20, 2017
Bell Work
Objective
-------------------------
Solve for x.
Students will learn about
1. 2x = 32
2. (1/8)x = 8
logarithms by studying the
3. 10 = 1
relationship between an
4. 15 = 15
exponential and logarithmic
x
x
function.
Jan 20­7:42 AM
7.4 Logarithms
Jan 20­7:45 AM
1/20 Day 1: Evaluating Logs
logarithm of y with base b: logb y = x Homework
**therefore bx = y
Ex. 1: Rewrite the logarithmic equation.
Rewrite the equation in exponential form.
a) log2 8 = 3
b) log4 1 = 0
c) log12 12 = 1
d) log1/4 4 = ­1
Ex. 2: Evaluate the logarithm.
a) log4 64
1. log3 81 = 4
2. log7 7 = 1
3. log14 1 = 0
4. log1/2 32 = ­5
b) log5 0.2
c) log1/5 125
d) log36 6
Jan 19­9:19 AM
common log: a logarithm with base 10 written as log
**log10 x = log x
natural log: a logarithm with base e written as ln
**loge x = ln x
Ex. 3: Evaluate common & natural logs.
Jan 19­9:38 AM
Homework
Evaluate the logarithm. Use a calculator if necessary.
5. log2 32 = a) log 8 = 6. log27 3 = b) ln 0.3 = 7. log 12 = 8. ln 0.75 = Jan 19­10:04 AM
Jan 19­9:38 AM
1
7.4 Day 1.notebook
January 20, 2017
Ex. 4: Inverse Functions: The wind speed s (in mph) near the center of a tornado can be modeled by
s = 93 log d + 65
g(x) = logb x is the inverse of f(x) = bx.
therefore...
g(f(x)) = logb bx = x
where d is the distance (in mi) that the tornado travels. In 1925, a tornado traveled 220 miles through 3 states. Estimate the wind speed near the tornado's center.
b
a) 10 log 4 = b) log5 25x = Jan 19­2:58 PM
You Practice!
Ex. 6: Find the inverse of the function.
a) y = 6x
5
= f(g(x)) = blog x = x
Ex. 5: Simplify the expression.
Jan 19­10:07 AM
7
and
b) y = ln (x + 3)
= log25 z
log7 x
log3 81x = log2 32x =
Jan 20­10:07 AM
Jan 20­12:01 PM
Wrap It Up...
You Practice!
1. Explain what a logarithm is.
y = log8 x
y = 0.4
x
2. What is special about a common and natural log?
y = ex + 2
y = 6 + log x
Jan 20­9:55 AM
3. How do you find the inverse functions of logarithmic functions?
Jan 19­3:06 PM
2
7.4 Day 1.notebook
January 20, 2017
Homework
Simplify the expression.
9. 8log x
11. log2 64x
10. log7 7­3
12. eln 20
8
Find the inverse of the equation.
13. y = 4x
14. y = ln (x ­ 5)
Jan 19­9:38 AM
3