Exercise 46 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.

5^(8(x-1)) = 625^(2x-2)

WritePow

Write as a power

5^(8(x-1)) = (5^4)^(2x-2)

PowPow

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

5^(8(x-1)) = 5^(4(2x-2))

Distr

Distribute 8

5^(8x-8) = 5^(4(2x-2))

Distr

Distribute 4

5^(8x-8) = 5^(8x-8)

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. 5^(8x-8) = 5^(8x-8) ⇔ 8x-8 = 8x-8 Finally, we will solve the equation 8x-8 = 8x-8 by subtracting 8x from both sides of the equation. 8x-8 = 8x-8 ⇔ -8=-8 ✓ Notice 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

Exercise 46 Page 304

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