Exercise 44 Page 304

Rewrite the terms so that they have a common base.

No solution.

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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

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Write as a power

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

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

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

Now we have two equivalent expressions with the same base. According to the Property of Equality for Exponential Equations, 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 e

quation 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

Exercise 44 Page 304

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