MI III Test on Logarithms
Name
NO CALCULATOR
Give exact answers whenever possible. Show significant steps.
1.
[4 pts]
Solve for x:
a.
log2  x  5  log2  x  3  log2 (3)
[3 pts]
b.
2.
xlog( x )  10, 000
Given u  logb (2) , v  logb (5) and w  logb (7) , then
logb (700) 
b.
logb (2  5  7) 
[3 pts ea]
a.
3.
[4 pts]
Write as a log of a single simplified expression with no negative exponents:
2 log 2  x 2  16   log 2  x  4   log 2  x  4 
Logs v1. p.1
Rev. S12
4.
Solve for x:
[3 pts]
5.
5  e 2 x  75e3
Explain why the graphs of the functions g ( x)  log  x 3  and h( x)  3log  x  are the same, while
the graphs of f ( x)  log  x 2  and k ( x)  2log  x  are not the same?
[4 pts]
6.
How long will it take for $10,000 to double in value if it is placed in a savings account that earns
2.25% interest, compounded monthly? Express your answer in terms of logarithms (any base).
7.
Determine the function f 1 ( x) , given f ( x)  35 x  2 .
[3 pts]
[3 pts]
Logs v1. p.2
Rev. S12
8.
Prove: log 3 n  x 3   9  log n  x  . You may use log rules and/or the definition of logs (your
choice!)
[4 pts]
9.
Solve for x:


log 2 log3  log 4  x    0
[3 pts]
10.
[2 pts]
If logb  a   0, what can be said about the value of a?
Logs v1. p.3
Rev. S12
10.
Graph y   log3  x  6 . Label at least 2 integer-valued points.
[5 pts.]
11.
[4 pts.]
Domain: __________________
Range: ________________________
Graph log  y   log  x  2  log 3
Domain: __________________
Range: ________________________
Logs v1. p.4
Rev. S12