Properties of Common Logs
Name 
Property

Example 
Log of a
Product 
log uv = log
u + log v 
log 5x = log
5 + log x 
Log of a
Quotient 


Log of a
Power 
log u^{n} = n
Â· log u 
log 4^{2} = 2
Â· log 4 

10^{ log u}
= u 
10^{ log 7}
= 7 
Here are three special cases involving common logs:
â€¢ log1 = log_{10} 1 = 0 because 10^{0} = 1.
â€¢ log10 = log_{10} 10 = 1 because 10^{1} = 10.
â€¢ log10^{n} = log_{10} 10^{n} = n because log10^{n}
= n Â· log 10 = n
Â· 1 = n.
Example 1
Write
as an equation containing two logs.
Solution
The right side contains the log of quotient. 

Use the Log of Quotient Property. 
L = 10 Â· (log I  log I_{0}) 
So
can be written as L = 10 Â· (log I  log I_{0}).
Note:
Notice that logI  logI_{0} must be in
parentheses since
was
multiplied by 10.
