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This printable supports Common Core Mathematics Standard HSF-BF.B.5, HSF-LE.A.4

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Solving Exponential Equations, #2 (Grades 11-12)

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Solving Exponential Equations, #2

Instructions: Assume that $log$ is base 10 and $ln$ is base $e$.

1.
What is the exact solution to $8*2^x = 3 ?$
1. $x = log_2(3/8)$
2. $x = log_2(3)/8$
3. $x = log_2(3/16)$
4. $x = log(3/8)$
2.
Solve exactly. $3*e^(2x) = 9$
1. $x = log(3/2)$
2. $x = 1/3 ln(9/2)$
3. $x = ln(3/2)$
4. $x = 1/2 ln(3)$
3.
What is the exact solution to $10^(4x) = e^2 ?$
1. $x = 1/2 ln(e)$
2. $x = 1/2 log(e)$
3. $x = 2log(e/2)$
4. $x = log(e/2)$
4.
Find the exact solution to the following equation. $2*2^x = 5$
1. $x = log(5/2)$
2. $x = 1/2 log(5)$
3. $x = log(5/2)/log(2)$
4. $x = log_2(5)$
5.
What is the exact solution to the equation $7e^(3x) = 1 ?$
1. $x = 0$
2. $x = 1/3 ln(1/7)$
3. $x = ln(1/21)$
4. $x = log(1/21)$
6.
Solve exactly. $1/2 *10^{12x} = 8$
1. $x = ln(4/3)$
2. $x = log(4/3)$
3. $x = 1/3 log(2)$
4. $x = log(1/3)$
7.
Find the exact solution to the following equation. $-3 * 2^{-5x} = -1/3$
1. $x = -2/5 log_2(1/3)$
2. $x = log_2(1/45)$
3. $x = log_2(-1/45)$
4. No solution.
8.
Solve exactly. $e^(1/2 x) = 7$
1. $x = log(7/2)$
2. $x = ln(7/2)$
3. $x = 2 ln(7)$
4. $x = 1/2 ln(7)$
9.
Find the exact solution to $18 * 2^x = 10$.
1. $x = ln(5/9) / ln(2)$
2. $x = ln(5/9)$
3. $x = 1/2 log(5/9)$
4. $x = 1/18 ln(10)$.
10.
What is the exact solution to $2^x = 10^e ?$
1. $x = log_2(10^e)$
2. $x = ln(10^e)$
3. $x = log(10^e)$
4. $x = 1/2 log(10^e)$
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