Question

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

Answer 1

B.
`\displaystyle (-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) = (1)/(b^m)`

Explanation:

Step 1: Define

Identify

`\displaystyle \bigg( (1)/(4) \bigg)^(x + 1) = 32`

Step 2: Solve for x

1. Rewrite:
   `\displaystyle \bigg( (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 = (-5)/(2)`
6. [Subtraction Property of Equality] Subtract -1 on both sides:
   `\displaystyle x = (-7)/(2)`