MI 3
Log Quiz #2
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Solve the equation for x. Leave answer in terms of logs, simplified as much as possible.
1.
a.
3x  5
b. (1.025)2 x1  5
2. Use the Laws of Logarithms to simplify the expression:
log 5 ( x 2  y 2 )  log 5 ( x  y )
3.
Given p  log3 (2) , q  log3 (5) - Express the follow in terms of p, q if possible.
 25 
a. log 3  
 2 
 8 
 45 


b. log 3 
4. Solve for x:
a. log 2 ( x)  log 2 (2 x  3)  1
IMSA
b. log 2 ( x)  log( x 2 )  15
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)  log3 x
f ( x)  log3 ( x  4)  2
Domain =
Range =
Domain =
Range =
f ( x)  log3  3x   1
Domain =
Range =
f ( x)  log3 x  3
Domain =
Range =
1
x
6. Prove: log b     log b ( x)
IMSA
SP12