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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 45 Page 304

Rewrite the terms so that they have a common base.

No solution.

Practice makes perfect

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

4^(x+3) = 2^(2(x+1))

Write as a power

( 2^2 )^(x+3) = 2^(2(x+1))

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

2^(2(x+3)) = 2^(2(x+1))

Distribute 2

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

Now, we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 2^(2x+6) = 2^(2x+2) ⇔ 2x+6 = 2x+2 Finally, we will solve the equation 2x+6 = 2x+2 by substituting 2x from both sides of the equation. 2x+6 = 2x+2 ⇔ 6 ≠ 2 * Note that the equation produces a false statement for all values of the variable x. Therefore, there are no solutions to the equation.

Subchapter links

Communicate Your Answer p.299

Monitoring Progress p.300-302

Exercises p.303-304