Mathematical Investigations III
Name:
Mathematical Investigations III
Logarithms
Practice 2
1.
2.
3.
4.
5.



Let f x  10 x
Let g x  log x
Domain:
Domain:
Range:
Range:
Find the domains of each of the following.
h x  log 2 x  5
a.
b.
j x  log x 2  3x
Find the ranges of each of the following.
k x   log x  2
a.
b.
m x  log x  1  2
Find:
a.
log3 34
b.
log5 5x 1
c.
2 log2 (32)
d.
3log3 (81)















 

Again with f x  10 x and g x  log x , find
a.
  
g f x 
b.
Logs 8.1
  
f g x 
Rev. S03
Mathematical Investigations III
Name:
9000
x
2
4
8
16
32
y
y
2
16
128
102 4
819 2
8000
7000
6000
5000
Data was collected and plotted.
4000
It was not clear what type of function was
represented by this data.
3000
Is it y  ax 2 or y  ax 3 or y  ax 4 ? or is it
2000
exponential, y  ab , or some other function
entirely?
x
1000
0
0
5
10
15
20
25
30
35
Sometimes, we can get a better idea about the nature of the function represented by the data if we
use logarithms. Let's create a table that consists of the log of each x value and the log of each y
value for each pair of data values. Since there are mostly powers of 2 in the data, let's use log
base 2. Complete the table and then graph the resulting ordered pairs of values.
U= log2(x)
V = log2(y)
V
log2(y)
U
log2(x)
Find the equation of your new graph in terms of U and V


Substitute U  log 2 x , and V  log 2 y
Transform the equation to write y as a function of x, eliminating
the logs to determine the function for the original data.
Logs 8.2
Rev. S03