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If 7^(2x) = 49, what is the value of x? (2023)

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Question: If 7^(2x) = 49, what is the value of x? (2023)

Options:

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Correct Answer: 1

Exam Year: 2023

Solution: 

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

If 7^(2x) = 49, what is the value of x? (2023)

Practice Questions

Q1
If 7^(2x) = 49, what is the value of x? (2023)
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Questions & Step-by-Step Solutions

If 7^(2x) = 49, what is the value of x? (2023)
  • Step 1: Recognize that 49 can be rewritten as a power of 7. Since 7^2 = 49, we can replace 49 in the equation.
  • Step 2: Rewrite the equation: 7^(2x) = 7^2.
  • Step 3: Since the bases (7) are the same, we can set the exponents equal to each other: 2x = 2.
  • Step 4: Solve for x by dividing both sides of the equation by 2: x = 2 / 2.
  • Step 5: Simplify the result: x = 1.
  • Exponential Equations – The question tests the ability to solve equations involving exponents by recognizing equivalent bases.
  • Properties of Exponents – It assesses understanding of how to manipulate and equate exponents when the bases are the same.
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