Logarithms And Logarithmic Functions Worksheet With Answers Page 20
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27log
51; sample answer: log
51 equals a little more
Never; if zero were in the domain, the equation
7
7
y
than 2. log
61 equals a little less than 2. log
71
would be y = log
0. Then b
= 0. However, for any
8
9
b
real number b, there is no real power that would let
equals a little less than 2. Therefore, log
51 is the
7-3 Logarithms and Logarithmic Functions
7
y
b
= 0
greatest.
62. ERROR ANALYSIS Betsy says that the graphs of
64. OPEN ENDED Write a logarithmic expression of
all logarithmic functions cross the y-axis at (0, 1)
the form y = log
x for each of the following
b
because any number to the zero power equals 1.
conditions.
Tyrone disagrees. Is either of them correct? Explain
a. y is equal to 25.
your reasoning.
b. y is negative.
SOLUTION:
c. y is between 0 and 1.
Tyrone; sample answer: The graphs of logarithmic
d. x is 1.
functions pass through (1, 0) not (0, 1).
e . x is 0.
ANSWER:
SOLUTION:
Tyrone; sample answer: The graphs of logarithmic
Sample answers:
functions pass through (1, 0) not (0, 1).
a. log
33,554,432 = 25;
2
63. REASONING Without using a calculator, compare
b.
log
51, log
61, and log
71. Which of these is the
7
8
9
greatest? Explain your reasoning.
c.
SOLUTION:
d. log
1 = 0;
7
log
51; Sample answer: log
51 equals a little more
7
7
e. There is no possible solution; this is the empty set.
than 2. log
61 equals a little less than 2. log
71
8
9
ANSWER:
equals a little less than 2. Therefore, log
51 is the
7
Sample answers:
greatest.
a . log
33,554,432 = 25;
2
ANSWER:
b.
log
51; sample answer: log
51 equals a little more
7
7
than 2. log
61 equals a little less than 2. log
71
c .
8
9
equals a little less than 2. Therefore, log
51 is the
d . log
1 = 0;
7
7
greatest.
e . There is no possible solution; this is the empty set.
64. OPEN ENDED Write a logarithmic expression of
65. FIND THE ERROR Elisa and Matthew are
the form y = log
x for each of the following
evaluating
Is either of them correct? Explain
b
conditions.
your reasoning.
a. y is equal to 25.
b. y is negative.
c. y is between 0 and 1.
d. x is 1.
e . x is 0.
SOLUTION:
Sample answers:
a. log
33,554,432 = 25;
2
b.
c.
d. log
1 = 0;
7
e. There is no possible solution; this is the empty set.
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Page 20
ANSWER:
Sample answers:
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