Name _______________________________________ Date _____________________________________________
Algebra II & Trigonometry
Logarithm Review WS
2. If f x   log x , evaluate f 1000  .
1. Solve for x: logx 16  4
3. Evaluate loga a
1
4. Write as a single logarithm: ln 2  3 ln x  ln b
2
5. If x  log2 6 , find the value of x, to the nearest
thousandth.
6. If f x   log3 x , what are the domain and range of
f x  ?
Domain: { x |
}
7. Solve for x:
Range: { y |
log x  logx  3  1 .
}
8. If logx 2 125  3 , find x.
9. Solve for x: logx  2  log2x  3  2 log x
10. Evaluate logb 1
a b
, which expression is equivalent to log x ?
cd
1
loga  log b  log c  logd
2
1
log a  log b  log c  log d
2
1
1
log a  log b  log c  log d
2
2
1
log a  log b  log c  log d
2
If ln a  x and ln b  y , then ln ab is equal to
1
1
1
xy
(3) x  y
2
2
2
1
1
1
xy
(4) x  y
2
2
2
11. If x 
(1)
(2)
(3)
(4)
14.
(1)
(2)
12. The inverse of y  10 x is obtained by reflecting
y  10 x in the line
(1) y = x
(2) y = –x
(3) y = 0
(4) x = 0
13. The graph of y  log4 x lies entirely in quadrants
(1) I and II
(3) III and IV
(2) II and III
(4) IV and I
1
15. If logx 3  , what is the value of x?
4
(1) 81
(2) 27
1
(3) 3
4
4
(4) 3
16. The equation y  a x expressed in logarithmic form
is
(1) y  loga x
(3) x  logy a
(2) x  loga y
(4) a  logy x
17. If log 6 = a, then log 600 =
(1) 100a
(2) a + 2
(3) a – 2
(4) 2a
18. What is the inverse of y  log4 x ?
(1) x  4 y
(2) y  4 x
(3) x  y 4
(4) y  x 4
19. Bacterial being grown for research programs at a university have a population modeled by the function B(t )  1.252t
where B(t) is in tens of thousands of bacteria and t represents the time in hours. After how many hours will the bacteria
population reach 1,000,000? (Round to the nearest tenth of an hour.)
20. The number of Canadian geese roaming the sports fields in one school district grows every year according to the
function Gt   241.2314 t where t is years since 2008. The Parent-Teacher Association has suggested hiring dogs
to chase the geese, but the dog squads will not work with geese populations fewer than 70. In what year can the
county hire the geese chasers?
21. The percentage of the United States population that is foreign-born is growing at an exponential rate. The function is
represented by the equation P t   4.5907e 0.027t where P is in millions and t is the number of years since 2000. In
what year did the number of people born outside the United States double their population of 2000?
22. Environmentalists in Ireland are concerned about the growth of the leprechaun population, represented by the function
Lt   1,2081.265 t where t is the number of years since 2010. Since the leprechauns live at the base of rainbows, an
increase in leprechauns without a corresponding increase in rainbows will be detrimental to the survival of the
leprechauns. If there are only enough rainbows for 10,000 leprechauns, how many years does the government have to
solve this problem?