Exercise 45 Page 304

Rewrite the terms so that they have a common base.

No solutions

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))

WritePow

Write as a power

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

PowPow

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

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

Distr

Distribute 2

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

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. 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 * Notice 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 45 Page 304

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