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Big Ideas Math Integrated I, 2016 View details

4. Solving Exponential Equations

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Exercise 4 Page 303

If both sides of the equation are equal, the exponents must also be equal.

x=12

Practice makes perfect

To solve the given exponential equation, note that we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 7^(x-4) = 7^8 ⇔ x-4 = 8Finally, we will solve the equation x-4 = 8 by adding 4 to both sides of the equation. x-4 = 8 ⇔ x=12 To check our answer, we will substitute 12 for x in the given equation.

7^(x-4) = 7^8

Substitute

x= 12

7^(12-4) ? = 7^8

SubTerm

Subtract term

7^8 = 7^8 ✓

Since substituting 12 for x in the given equation produces a true statement, x=12 is the solution to our equation.