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What is the value of log4(16)?
What is the value of log4(16)?
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What is the value of log4(16)?
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log4(16) = log4(4^2) = 2.
Questions & Step-by-step Solutions
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Q: What is the value of log4(16)?
Solution:
log4(16) = log4(4^2) = 2.
Steps: 7
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Step 1: Understand what log4(16) means. It asks, 'To what power do we raise 4 to get 16?'
Step 2: Recognize that 16 can be written as 4 raised to a power. Specifically, 16 is the same as 4^2.
Step 3: Rewrite log4(16) using this information: log4(16) = log4(4^2).
Step 4: Use the property of logarithms that says logb(a^c) = c * logb(a). Here, b is 4, a is 4, and c is 2.
Step 5: Apply this property: log4(4^2) = 2 * log4(4).
Step 6: Since log4(4) equals 1 (because 4 raised to the power of 1 is 4), we have: log4(4^2) = 2 * 1.
Step 7: Therefore, log4(16) = 2.
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