Mathematical Investigations III
Name:
Mathematical Investigations III
Logarithms
Practice 1
1.
Re-write each logarithmic equation as an exponential equation and find w.
log
 
1000 w
exp
w
log10 10  w
log10
log
 
log 2  w
log 32768 w
log10
exp
w
exp
w
w
 
log 1 w
log 1 32  w
log
exp
w
 
log 625 w
exp
w
log5 25  w
5
5
 
log5 5100  w


log5 1  w
log5 5a  w

exp
2
log 5 5  w
log
log
2
2
5
w
log 2 1 2  w
2

log 125 w
log 3125 w
 
0.01 w
exp
log10 100  w
log 2 16  w
log
log
exp
w
log a a  w
log
 
log a 1 a  w
 
log a  w
 
log a a  w
log a a x  w
log a a y  w
x y
x
a
y
a
Logs 2.1
Rev. S03
Mathematical Investigations III
Name:
To evaluate a logarithm, think exponent!
For example, to evaluate log 3 81 , ask: What power of 3 will give you 81? So log 3 81  4 .
2.
Find the value of each log:
a. log 2 32 
b.
 1
log6   
 6
 1
d. log3   
 9
e.
h.
log5 5n 
 

g. loge e7 
 
c.
log 2 512 
log8 2 

f.
log10 1,000,000 

i.
log n n5 



 
j. Why is it impossible to evaluate log 2 8  ?
3.
Without using a calculator, estimate the value of each log given below between two
consecutive integers.
For example: log 2 11  is between 3 and 4, since 23  8 and 2 4  16 .
 
 
a. log 2 40
 
d. log10 300
4.
 
 1
c. log 2  
 3

f. log10 .03
 
e. log10 3
Use your calculator to estimate each log value to three decimal places.
(Remember, on a calculator, log x  log10 x .) Watch for patterns.

 
a. log10 300
d.
5.
b. log 3 40
b. log10

log10 .3

30
c. log10 3
 
f. log10 .003

 
e. log10 .03
Watch for some connections as you evaluate each of the following:
 
a1. log 2 32 




 


a2. log 2 8  log 2 4 

b1. log 3 9 g27 

b2. log3 9  log3 27 
c1. log5 57 
c2. log5 54  log5 53 
 128 
d1. log 2 

 16 
d2. log 2 128  log 2 16 
 
e1. log5 25a 
 
 
 
e2. a glog5 25 
Logs 2.2
Rev. S03