MI 3
Log Quiz #2
Name: _______________________
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Show your work to get full credit:
1. Find the value of (log125 5)


b2
2. Expand log  2

 c  2c  1 
3.
log5 125
1
using the laws of logarithms.
Given p  log3 (2) , q  log3 (5) and r  log3 (49) , express the following in terms of p, q and
r if possible.
 125 
a. log 3 

 12 
 4
 7 


b. log 3 
4. Solve for x:
a. logb ( x)  logb (2 x  3)  logb (2)
b. log 2 ( x)  log( x 2 )  15
5. Find the inverse, f 1 ( x) , given that f ( x)  3 102 x 1 .
IMSA
Sp12
IMSA
SP12
5. Graph each of the following functions. In each case label the scales on the x- and y- axes clearly and
label at least three points.
f ( x)  log5 ( x)
Domain =
Range =
f ( x)  log 2  x   2
Domain =
Range =
f ( x)  log3 ( x  1)  3
Domain =
Range =
f ( x)  log3 x  2
Domain =
Range =
6. Prove the following. Clearly show your steps to get full credit.
IMSA
log a (b 4 )
log a4 (b) 
.
16
SP12