Algebra 2 Test Review Logs and Exponentials
SHOW YOUR WORK ON A SEPARATE SHEET OF PAPER
Some values for the function 𝑓(𝑥) = 10𝑥 are given in
Table 1.
1.
6.
Let
and its inverse
. What is
?
Table 1
Table 2
7.
Solve the exponential equation.
8.
Solve
9.
Solve
10. Solve
11. Solve, round to the nearest hundredth.
Which function can generate all the values in Table 2?
𝑔(𝑥) = log 𝑥
a.
b.
. Round to the nearest ten-thousandth.
12. Use a graphing calculator. Solve
phing. Round to the nearest hundredth.
c.
by gra-
d.
13. The generation time G for a particular bacteria is the time
it takes for the population to double. The bacteria increase
2.
Below is a tabular representation of points on the logarithmic function 𝑓(𝑥) = log 𝑥 + 2.
x
.1
1
10
100
f  x
1
2
3
4
The function g  x  is the result of finding the inverse of
f  x  . Fill in the table below for the function g(x).
x
in population is shown by the formula
where t is the time period of the population increase, a is
the number of bacteria at the beginning of the time period,
and P is the number of bacteria at the end of the time period. If the generation time for the bacteria is 5 hours, if
they are left to increase how many will be in the colony in
4 hours? 60 hours? 100 hours? Round to the nearest
whole number.
14. Solve, round to the nearest ten-thousandth if necessary.
15. Solve
g  x
.
16. Solve
dredth if necessary.
17. Simplify
3.
Graph 𝑓(𝑥) = 2𝑥 and its inverse 𝑓 −1 (𝑥) = log 2 (𝑥).
,
. Round to the nearest hun-
.
18. Solve
. Round to the nearest thousandth.
19. Solve
essary.
. Round to the nearest tenth, if nec-
20. Solve
.
21. Solve the equation. Round to the nearest thousandth.
22. Solve the equation.
23. Solve the equation.
24. Solve the equation. Round to the nearest thousandth.
1
4.
What is the inverse of ℎ(𝑥) = log 2 (𝑥)
5.
What is the inverse of ℎ(𝑥) = log 5 (𝑥)
3
1
4
25. The sales of lawn mowers t years after a particular model
is introduced is given by the function
, where y is the number of mowers
sold. How many mowers will be sold 3 years after a
model is introduced? Round the answer to the nearest
whole number.