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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 43 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.

3^(3x+6) = 27^(x+2)

Write as a power

3^(3x+6) = ( 3^3 )^(x+2)

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

3^(3x+6) = 3^(3(x+2))

Distribute 3

3^(3x+6) = 3^(3x+6)

Now, we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 3^(3x+6) = 3^(3x+6) ⇔ 3x+6 = 3x+6 Finally, we will solve the equation 3x+6 = 3x+6 by subtracting 3x from both sides. 3x+6 = 3x+6 ⇔ 6=6 ✓ 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