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If log_5(25) = x, what is the value of log_5(5^x)?

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Question: If log_5(25) = x, what is the value of log_5(5^x)?

Options:

  1. x
  2. 2x
  3. x^2
  4. 5x

Correct Answer: x

Solution: 

log_5(5^x) = x.

If log_5(25) = x, what is the value of log_5(5^x)?

Practice Questions

Q1
If log_5(25) = x, what is the value of log_5(5^x)?
  1. x
  2. 2x
  3. x^2
  4. 5x

Questions & Step-by-Step Solutions

If log_5(25) = x, what is the value of log_5(5^x)?
Correct Answer: x
  • Step 1: Understand that log_5(25) = x means that 5 raised to the power of x equals 25.
  • Step 2: Rewrite 25 as 5^2. So, we have 5^x = 5^2.
  • Step 3: Since the bases are the same (both are 5), we can set the exponents equal to each other: x = 2.
  • Step 4: Now, we need to find log_5(5^x). Substitute x with 2: log_5(5^2).
  • Step 5: Use the property of logarithms that says log_b(b^y) = y. Here, b is 5 and y is 2.
  • Step 6: Therefore, log_5(5^2) = 2.
  • Logarithmic Properties – Understanding the properties of logarithms, particularly that log_b(b^a) = a.
  • Change of Base – Recognizing how to manipulate logarithmic expressions using known values.
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