Exponents Homework #3, Aat Unit 5 - February 16th/17th Page 2
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1
24. Apply the change of base formula to rewrite each logarithm using both natural and common logarithms:
Common log equivalent
Original logarithm
Natural log equivalent
log
27
3
log
216
6
5. For each equation, find the value of ��.
1
a. log
�� = −2
�� = ____________
b. log
�� =
�� = ____________
8
36
2
c. log 10,000 = ��
�� = ____________
d. log
9 = ��
�� = ____________
3
( 4 − 3�� ) = 3
e. log
�� = ____________
f. log
−16 = ��
�� = ____________
4
2
6. Determine if each of the following statements is true or false. For false statements, explain why or give a
counterexample.
a. T / F
The argument of a log can be a negative number.
b. T / F
The value (output) of a log can be a negative number.
log
0 = 1
c. T / F
2
log
1 = 0
d. T / F
2
��
��
5(7)
= 35
e. T / F
��
In the relationship ��
= ��, if �� is greater than ��, �� must be greater than 1.
f.
T / F
��
In the relationship ��
= ��, if �� is less than ��, �� must be a negative number.
g. T / F
7. Consider the paper-folding problem, where you start with a single sheet of paper and repeatedly fold it in half. The
��
number of layers of paper after �� folds can be modeled with the function �� ( �� ) = 2
.
a. How many layers of paper will there be after 8 folds?
b. Set up an equation to determine how many folds you would have to make in order to get 2,048 layers of paper.
Then, write the exponential equation in logarithmic form and solve.
c. Set up an equation to determine how many folds you would have to make in order to get 1,000 layers of paper.
Then, write the exponential equation in logarithmic form (you don’t need to solve!).
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