Mathematical Investigations III
Name:
Mathematical Investigations III
Logarithms
Practice 5
1.
Solve for x.
a.
log6 x 2  3  1


b.
log 5log 7 log 9 x


d.
3x  51.6
c.
log8 3x  5  0
e.
x
5
7

 
log 1 16 log 1 125
log 2 4  log5 25
2
2.
3
5
If the perimeter of the rectangle is no more
than 6, determine the domain for x.
log(x)
log(20)
3.
a.

If f x  2 x  3 , find f
1
x .
b.
Logs 12.1




If g x  log 3 x  2 ,find g 1 x .
Rev. S07
Mathematical Investigations III
Name:
4.
Given isosceles trapezoid ABCD with
AD = BC, AB  log 9 8 , and EC  log 9 72

log9(8)
A
 
a. Find DE.
log8(81)
E
D
b. Find the area of ABCD, and leave your
answer simplified with log base 2.
5.
Which is greater? Justify your answer.
log(2) + log(4) + log(6) + log(8) or log(2 + 4 + 6 + 8)
6.
Graph the following:
(Watch the domains!)
a. log y  log 2x  6

B

log9(72)
C


b. log y   x


 
c. log y  log x  log x
7.
 

Explain why the graphs of y1  log x 2 and y2  2 log x are not the same.
Logs 12.2
Rev. S07
Mathematical Investigations III

Name:

log x  1  2 x  4
8.
Use graphing to solve for x:
9.
a. Can a triangle exist with sides of length 2, 3, and 6? Why?
b. Can a triangle exist with sides log(2), log(3), and log(6)? Why?
c. Can a triangle exist with sides log(2), log(3), and log(5)? Why?
10.
Given the graph of g, sketch the graph of the other functions. Label intercepts.
yg x
y g x
yg x


 
 
yg x3
1

yg x
11.

y  g x

Solve for x.
a.
  
log3 log 2 x  2
b.
  
log 2 log3 x  2
11. (continued)
Logs 12.3
Rev. S07
Mathematical Investigations III
c.

Name:
10  log x
x

d.


log x  ln x
e x  e x
. Find a so that f a  3 .
2

12.
Let f x 
13.
Radioactive polonium has a half-life of 140 days. How many days will it take for 70% of
a sample to decay? (Hint: Check the MI II exponential unit.)
14.
A beverage company introduces a new soda, 6-Down Clear. During their big advertising
campaign, revenue is about $200,000 per day. When the advertising stops, revenue
begins to drop about 1.5% per day. They plan to start advertising again when revenue
drops to $120,000. After how many days will this be necessary?
Logs 12.4
Rev. S07