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If 7^(x) = 1/49, what is the value of x? (2023)

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Question: If 7^(x) = 1/49, what is the value of x? (2023)

Options:

  1. -2
  2. 2
  3. 0
  4. -1

Correct Answer: -2

Exam Year: 2023

Solution: 

Since 1/49 can be expressed as 7^(-2), we have 7^x = 7^(-2), thus x = -2.

If 7^(x) = 1/49, what is the value of x? (2023)

Practice Questions

Q1
If 7^(x) = 1/49, what is the value of x? (2023)
  1. -2
  2. 2
  3. 0
  4. -1

Questions & Step-by-Step Solutions

If 7^(x) = 1/49, what is the value of x? (2023)
  • Step 1: Start with the equation 7^(x) = 1/49.
  • Step 2: Recognize that 49 is the same as 7^2, so 1/49 can be written as 1/(7^2).
  • Step 3: Rewrite 1/(7^2) as 7^(-2) because 1/a^b = a^(-b).
  • Step 4: Now the equation looks like this: 7^(x) = 7^(-2).
  • Step 5: Since the bases (7) are the same, we can set the exponents equal to each other: x = -2.
  • Exponential Equations – Understanding how to manipulate and solve equations involving exponents.
  • Properties of Exponents – Using the property that if a^m = a^n, then m = n for the same base a.
  • Negative Exponents – Recognizing that 1/a^n can be rewritten as a^(-n).
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