Properties of Logarithms

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Show your work for each problem.

1.
What is $\log_6 1$ ?
1. a)it is undefined
2. b)0
3. c)6
4. d)1
2.
Evaluate $\log_8 8$ .
3.
Evaluate $\log_5 1 + \log_5 5 + \log_5 25$ .
4.
Simplify $\log_3(3^7)$ .
5.
Simplify $5^{\log_5 9}$ .
1. a)9
2. b)45
3. c)5
4. d) $\log_5 9$
6.
Evaluate $\log 10000$ (common logarithm, base 10).
7.
Evaluate $\log_2 32$ .
8.
Which of these logarithms is undefined?
1. a) $\log_5 5$
2. b) $\log_3(-9)$
3. c) $\log_4 \frac{1}{4}$
4. d) $\log_2 1$
9.
For which $x$ is $\log_3(x - 4)$ defined? Find the smallest whole number $x$ that is allowed.
10.
Evaluate $\log_5 \frac{1}{25}$ .
11.
Simplify $2^{\log_2 5} \cdot 3^{\log_3 4}$ .
12.
If $\log_4 M = \log_4 20$ , what is $M$ ?
1. a)4
2. b)5
3. c)20
4. d)80
13.
Solve $\log_3(x + 4) = \log_3 10$ .
14.
Evaluate $\log_3 \frac{1}{9} + 6^{\log_6 11}$ .
15.
Which statement is true for every allowed base $b$ ?
1. a) $\log_b 0 = 0$
2. b) $\log_b(b^x) = x$ for every real $x$
3. c) $\log_b 1 = 1$
4. d) $b^{\log_b x} = x$ for every real $x$
16.
Evaluate $\log_2(8^4)$ . First write $8$ as a power of $2$ .
17.
Solve $\log_5(x^2 - 6) = \log_5 x$ .
18.
Evaluate $\log_4 8$ by writing $8$ as a power of $4$ .