Name Date
WORKSHEET 8.16: SOLVING EXPONENTIAL EQUATIONS
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An exponential equation is an equation that includes a variable in the exponent. Follow the
steps below to solve an exponential equation:
- Rewrite each side of the equation so that the bases are the same, if necessary.
- Write an equation stating that the two exponents are equal.
- Check your answer by substituting the values in the original equation.
EXAMPLES
23 x= 2 x−^192 = 3 x
Solve forx:3x=x− 1 Rewrite the equation: (3^2 )^2 = 3 x→ 34 = 3 x
2 x=−1Solveforx: x= 4
x=−
1
2
Check: 92 = 34 or 81 = 81
Check: 2 −
(^32)
= 2 −
(^12) − 1
DIRECTIONS: Solve.
- 34 x= 32 x−^2 2. 5 x−^1 = 25 3. 49 = 73 x−^1
- 4 = 16 x−^1 5. 2 x+^1 =
√
4 6. 8 = 2 x−^2
CHALLENGE:Myles rewrote 9^4 x=81 as 9^4 x= 92 .Clairerewrote9^4 x=81 as
(3^2 )^4 x= 34 or 3^8 x= 34. In each case, the answer isx=
1
2
. Who is correct?
Explain your answer.
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Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.