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34kurt
3 years ago
10

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

Mathematics
1 answer:
GarryVolchara [31]3 years ago
3 0

Answer:

B.  \displaystyle \frac{-7}{2}

General Formulas and Concepts:

<u>Pre-Algebra</u>

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<u> </u>

<u>Algebra I</u>

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

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

<em />\displaystyle \bigg( \frac{1}{4} \bigg)^{x + 1} = 32<em />

<em />

<u>Step 2: Solve for </u><em><u>x</u></em>

  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}
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