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If log_5(25) = x, what is the value of log_5(5^x)?
If log_5(25) = x, what is the value of log_5(5^x)?
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Practice Questions
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Q1
If log_5(25) = x, what is the value of log_5(5^x)?
x
2x
x^2
5x
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log_5(5^x) = x.
Questions & Step-by-step Solutions
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Q: If log_5(25) = x, what is the value of log_5(5^x)?
Solution:
log_5(5^x) = x.
Steps: 6
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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.
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