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If log_7(49) = x, what is the value of x?

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Question: If log_7(49) = x, what is the value of x?

Options:

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Correct Answer: 2

Solution: 

Since 49 = 7^2, log_7(49) = 2, thus x = 2.

If log_7(49) = x, what is the value of x?

Practice Questions

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If log_7(49) = x, what is the value of x?
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Questions & Step-by-Step Solutions

If log_7(49) = x, what is the value of x?
Correct Answer: 2
  • Step 1: Understand the question. We need to find the value of x in the equation log_7(49) = x.
  • Step 2: Recall the definition of logarithms. log_b(a) = c means that b^c = a.
  • Step 3: Identify the base and the number in our case. Here, the base is 7 and the number is 49.
  • Step 4: Rewrite 49 as a power of 7. We know that 49 = 7^2.
  • Step 5: Substitute this back into the logarithm. So, log_7(49) becomes log_7(7^2).
  • Step 6: Use the property of logarithms that states log_b(b^c) = c. Therefore, log_7(7^2) = 2.
  • Step 7: Conclude that x = 2.
  • Logarithms – Understanding the relationship between exponents and logarithms, specifically how to express a number as a power of its base.
  • Exponential Equations – Recognizing that 49 can be rewritten as 7 raised to a power (7^2) to simplify logarithmic expressions.
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