Solving Exponential Equations

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Show your work for each problem.

1.
Solve $2^x = 16$ .
1. a) $4$
2. b) $8$
3. c) $14$
4. d) $2$
2.
Solve $3^x = 81$ .
3.
Solve $5^{x-1} = 125$ .
4.
Which equation is $4^x = 64$ written with base $2$ on both sides?
1. a) $2^{2x} = 2^6$
2. b) $2^{x+2} = 2^6$
3. c) $2^{2x} = 2^8$
4. d) $2^x = 2^6$
5.
Solve $5^x = \frac{1}{25}$ .
6.
Solve $3 \cdot 2^x = 96$ .
7.
Solve $8^x = 4$ . Write the answer as a fraction, like 3/4.
8.
Solve $9^x = \frac{1}{27}$ .
1. a) $-3$
2. b) $-\frac{3}{2}$
3. c) $\frac{3}{2}$
4. d) $-\frac{2}{3}$
9.
Solve $2^{3x} = \frac{1}{16}$ . Write the answer as a fraction, like -5/2.
10.
Solve $8^x = 32$ . Write the answer as a fraction, like 7/2.
11.
Solve $25^x = 125$ . Write the answer as a fraction, like 5/4.
12.
Solve $5 \cdot 3^{x+1} = 405$ .
13.
The solution of $2^x = 20$ is not a whole number. Between which two consecutive integers does it lie?
1. a)4 and 5
2. b)3 and 4
3. c)10 and 11
4. d)5 and 6
14.
Solve $4^{x+1} = 8^x$ .
15.
The equation $2^{x^2 - x} = 64$ has two solutions. What is the larger one?
16.
Solve $\left(\frac{1}{2}\right)^x = 8$ .
17.
Which equation has no solution?
1. a) $3^x = 1$
2. b) $2^x = \frac{1}{8}$
3. c) $4^x = 2$
4. d) $5^x = -25$
18.
The solution of $3^x = 50$ is not a whole number. What is the smallest whole number $n$ with $3^n > 50$ ?