Question

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What is the solution to this equation? (1/4)^x+1 =32

Answer 1

Answer:

B.  $\displaystyle \frac{-7}{2}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right  

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Algebra I

• Exponential Rule [Powering]:                                                                           $\displaystyle (b^m)^n = b^{m \cdot n}$
• Exponential Rule [Rewrite]:                                                                              $\displaystyle b^{-m} = \frac{1}{b^m}$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \bigg( \frac{1}{4} \bigg)^{x + 1} = 32$

Step 2: Solve for x

1. Rewrite:                                                                                                             $\displaystyle \bigg( \frac{1}{2^2} \bigg)^{x + 1} = 2^5$
2. Exponential Rule [Rewrite]:                                                                              $\displaystyle (2^{-2})^{x + 1} = 2^5$
3. Exponential Rule [Powering]:                                                                          $\displaystyle 2^{-2(x + 1)} = 2^5$
4. Set:                                                                                                                    $\displaystyle -2(x + 1)} = 5$
5. [Division Property of Equality] Divide -2 on both sides:                                $\displaystyle x + 1 = \frac{-5}{2}$
6. [Subtraction Property of Equality] Subtract -1 on both sides:                        $\displaystyle x = \frac{-7}{2}$