The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 8.16: SOLVING EXPONENTIAL EQUATIONS -------------------------------------------------------------------------------------

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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