16.2 Introduction to Logarithms

A logarithmic function is the inverse of an exponential function
o

Name_____________________
f ( x)  b x or y  b x is equivalent to
Thus x  b y is the same as y  logb x
Convert forms:
1.
log6 36  2
2.
logb n  23
3. 53 
1
125
Evaluate:
4.
log3 81
5.
log3 3
6.
7.
log 5
1
25
8.
log7 1
9. log6 65
log9 27
Solve
10. log4 x  3
11. log3 x  5
12. log x 9 
1
2
13. log5 25  x
14. log2 64  x
Product Rule: logb  MN   logb M  logb N


p
Power Rule: log b M  p log b M
 x
 25 


16. log 5 



  x  14  x  1 


17. log 
x3 x 2  1
1
log  x  9   4 log x
18. 3
19.
log x  log  x 2  1  log 7  log  x  2 
15. log x 6 
M
N
Quotient Rule: logb 
1
3

  logb M  logb N

Change of Base Formula logb M 
log a M
log a b