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If log_4(16) = x, what is the value of x?
If log_4(16) = x, what is the value of x?
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If log_4(16) = x, what is the value of x?
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log_4(16) = log_4(4^2) = 2.
Questions & Step-by-step Solutions
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Q: If log_4(16) = x, what is the value of x?
Solution:
log_4(16) = log_4(4^2) = 2.
Steps: 6
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Step 1: Understand that log_4(16) means 'to what power must 4 be raised to get 16?'
Step 2: Recognize that 16 can be written as 4 raised to a power. Specifically, 16 = 4^2.
Step 3: Rewrite the logarithm using this information: log_4(16) = log_4(4^2).
Step 4: Use the property of logarithms that states log_b(b^a) = a. Here, b is 4 and a is 2.
Step 5: Therefore, log_4(4^2) = 2.
Step 6: Conclude that x = 2.
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