KEY
Math 120, 123 Practice Quiz # 22 – Sections 11.5-11.6
Properties of Logarithms, Exponential and Logarithmic
Equations
In problems 1 and 2, use the properties of logarithms to expand the given expression.
1. log (6x2 + 12x + 6)
2. ln (e2 – 2e)3
log6 + 2log(x + 1)
3 + 3ln(e – 2)
In problems 3 and 4, use the properties of logarithms to combine the given expression into a
single logarithm.
3.
2
3 log( x  1)  log( 2 x  2)
3
4. 3 ln( x  1)  2 ln( x  2)  4 ln( x)
log( x  1) 2 / 3
2
ln
( x  1) 3 x 4
( x  2) 2
In problems 5 and 6, use the change of base property to expand the logarithmic
expressions and then evaluate the expression.
5. (log8125)(log1/58)
 log 125  log 8 



- 3
 log 8  log 15 
6.
log 4 36
1
log 4
6
 log 36 


 log 4  - 2
 log 1 

6
 log 4 


In problems 7-10, solve the given equation.
7. 4 2 x 1  64
2
8. e 0.07t  3  3.08
- 36.08
9. log2(8 – 6x) = 5
-4
10. log7(x + 1) + log7(x + 2) = log76
1
11. The number of computer infected by a virus t minutes after it first appears usually
increases exponentially. If the function N(t) = 100e0.077t represents the number of
computers infected after t hours.
a. How many computers will be infected after 2 hours? About 117 computers
b. How long will it take for 80,000 computers to be infected? About 87 minutes
12. When archaeologists found the Dead Sea Scrolls, they determined that the linen
wrapping had lost 22.3% of its carbon-14. How old was the linen-wrapping? 2086 years