Exercise 14 Page 303

Rewrite the terms so that they have a common base.

x=-4

Practice makes perfect

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

(1/4)^x = 256

1/a=a^(- 1)

(4^(-1))^x = 256

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

4^(-1* x) = 256

4^(- x) = 256

Write as a power

4^(- x) = 4^4

Now we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. \

begin{gathered} 4^{\text{-} x} = 4^4 \quad \Leftrightarrow \quad \text{-} x = 4 \end{gathered} Finally, we will solve the equation - x = 4.

- x = 4

.LHS /(-1).=.RHS /(-1).

x = -4

To check our answer, we will substitute -4 for x in the given equation.

(1/4)^x = 256

x= -4

(1/4)^(-4) ? = 256

1/a=a^(- 1)

(4^(-1))^(-4) ? = 256

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

4^(-1(-4)) ? = 256

- a(- b)=a* b

4^4 ? = 256

Calculate power

256 = 256 ✓

Since substituting -4 for x in the given equation produces a true statement, x=-4 is the solution to our equation.

Communicate Your Answer p.299

Monitoring Progress p.300-302

Exercises p.303-304

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