Algebra II
Name_
Exponential and Log Test Review
CALCULATOR SECTION
Date_
Pd.
a) How do you evaluate a log in your calculator if there is no base written?
b) What is this type of Log called from letter a?
Cs
c) How do you evaluate a log in your calculator if the base is not 10?
d) Write an example
\^\- 2-5
**J.— _
l
r for letter
----c: _
--------e) When you evaluate a log expression, what are you really finding
i>
f ) Logarithms and exponentials are
i </\ \s of each other.
g) The two critical points of the exponential parent function are
i) What is the base of a natural log?
fv^ f- 4-o
ft
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I O ( I ) C *. \) The two critical points of the logarithmic
what is it's approx. value?
' ' *^"
Evaluate the following common log expressions to 3 decimal places in your calculator.
1. log 25
2. Iog24
Evaluate using the Change Base Rule and a calculator. Round to 3 decimal places!
3. Iog5 81.2
2-132.
4. Log2 54
5. Logu 12
5^7^^
6. logu 19
(,t>ZC?
U
Solve each Logarithmic equation below. You may use a calculator.
= 31og2(3)-21og2(3)
8.
7.
5
Iog3 x - Iog3 4 = Iog3 12
9.
Iog4 (x - 5) + log, (3) = 2
10.
y -'
X
3
(2x - 6) + loge x - 2
11.
12.
*°
Solve for x using your calculator. Round answers to 2 decimal places.
14. 2.53x'5r 23.45
13. 1.95 X =55
15. H 4x
NON-CALCULATOR SECTION
a) What is the asymptote of the parent exponential function (y = bx) and tell whether it is horizontal or
vertical.
U "=- O
LLensOrQ*.}* /
b) List the asymptote of the parent logarithmic function ( y = I°§A x ) and tell whether it is horizontal or
vertical.
X^Q
c) Which transformations affect the asymptote of the parent exponential function?
j*t»T"/
6ive an
example:
d) Which transformations affect the asymptote
ymp
of the parent logarithmic function?
example:
)
I4of^o^l &*hh,•ive an
Graph the following exponential equations. Draw the asymptote as a dotted line. NO CALCULATOR.
16. y-
Is this an example of exponential ^owtpor decay? Explain.
/
Asymptote Eg:
\,
(.-^j^b )
Range:
*j "•-•
17.
vX-3
+5
^^
^j
Is this an example of exponential growth oifdecayl Explain.
Range:
Domain:
Asymptote Eg:
H ^S
Graph the following logarithmic equations. Draw the asymptote as a dotted line. NO CALCULTOR.
IL
18.
Domain:.
Asymptote Eq:_
Range::
( -O>
,-2-
19.
Domain:.
Range:
Asymptote Eq:_
Evaluate the following expressions. NO CALCULATOR.
Iog52 52
Iog 10 100
20.
Iog2
22.
21. Iog5125
23.
16
24.
log, 81
3
-M
Describe all 4 Log properties and write an example of each
• Product Property
Quotient Property
Power Property
o<?,X
h£| QA f^\•
Change of Base Property
~
P
HbO -
Condense the following expressions into a single logarithm. NO CALCULATOR.
51og 7 3--log 7 64 + -log 7 x
25.
31og 2 x + -log 2 ^-41og 2 15
26.
3s7r
27.
logs 5 +Iog3 2 - 2log3x
28. \4 25 - Iog4y + 3log4x
x3
H,
3 -?
Expand the expression completely using your log properties.
Iog3
29.
log
30.
x
/—
Iog5 5*lx
5xz2
,
~3
2x
Iog3 —
32.
5y
31.
33. Determine whether each is equation is a growth or decay exponential function:
a. f(x) = y
b. g(*) = fjl
c./i(x) = 6f|l
d. g(*) = (jV
3
Solve each exponential equation for x. Be sure to show all thinking and work.
493/7+1 =
34.
35.
f '
e./z(x) = fil
f.