MI III Test on Logarithms
Name
NO CALCULATOR
Give exact answers whenever possible. Show significant steps.
1.
[4 pts]
Solve for x:
a.
log2  2 x  4  log2  x   3
[3 pts]
b.
x 2log( x )  x 7
[3 pts]
c.
2log2  2 x   log2  x  4  log2  x  4  2
2.
[3 pts ea]
Given u  log(2) and w  log(7) , then
a.
log(0.0007) 
b.
Logs v1. p.1
log( 2800) 
Rev. S12
3.
Solve for x:
[3 pts]
4.
2  e 2 x  8  e3
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]
5.
Radioactive Pandyasium decays at a rate of 2.5% a year. Find the half-life of this substance.
Express your answer in terms of the natural logarithm, (ln).
[4 pts]
6.
Determine the function f 1 ( x) , given f ( x)  2log3 ( x  3) .
[3 pts]
Logs v1. p.2
Rev. S12
7.
Prove: log x3  5 x 2  
8.
Simplify:
2  log x  5
. You may use log rules and/or the definition of logs (your choice!)
3
[4 pts]

log 2 log3  log 4  64  

[3 pts]
9.
[2 pts]
If logb 10  1, what can be said about the value of b?
Logs v1. p.3
Rev. S12
10.
[5 pts.]
11.
[5 pts.]
Graph y  log 3  x  6  . Label at least 3 points including any intercepts.
Domain: __________________
Range: ________________________
Graph f ( x)  3log 2  x  2
Domain: __________________
Range: ________________________
Logs v1. p.4
Rev. S12