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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

4. Solving Exponential Equations

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Exercise 46 Page 304

Rewrite the terms so that they have a common base.

All real numbers.

Practice makes perfect

To solve the given exponential equation, we will start by rewriting the terms so that they have a common base.

5^(8(x-1)) = 625^(2x-2)

Write as a power

5^(8(x-1)) = (5^4)^(2x-2)

(a^m)^n=a^(m* n)

5^(8(x-1)) = 5^(4(2x-2))

Distribute 8

5^(8x-8) = 5^(4(2x-2))

Distribute 4

5^(8x-8) = 5^(8x-8)

Now, we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 5^(8x-8) = 5^(8x-8) ⇔ 8x-8 = 8x-8 Finally, we will solve the equation 8x-8 = 8x-8 by subtracting 8x from both sides of the equation. 8x-8 = 8x-8 ⇔ -8=-8 ✓ Note that the equation produces a true statement for all values of the variable x. Therefore, the solutions to the equation are all real numbers.

Subchapter links

Communicate Your Answer p.299

Monitoring Progress p.300-302

Exercises p.303-304