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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 44 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.

3^(4x+3) = 81^x

Write as a power

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

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

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

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^(4x+3) = 3^(4x) ⇔ 4x+3 = 4x Finally, we will solve the equation 4x+3 = 4x by substituting 4x from both sides. 4x+3 = 4x ⇔ 3 ≠ 0 * 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