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What is the value of log_4(64)?
What is the value of log_4(64)?
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What is the value of log_4(64)?
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log_4(64) = log_4(4^3) = 3.
Questions & Step-by-step Solutions
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Q: What is the value of log_4(64)?
Solution:
log_4(64) = log_4(4^3) = 3.
Steps: 7
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Step 1: Understand what log_4(64) means. It asks, 'To what power do we raise 4 to get 64?'
Step 2: Rewrite 64 as a power of 4. We know that 4 can be written as 4^1, 4^2, 4^3, etc.
Step 3: Calculate 4^3. This means 4 * 4 * 4, which equals 64.
Step 4: Now we can say that 64 is the same as 4^3.
Step 5: Substitute back into the logarithm: log_4(64) = log_4(4^3).
Step 6: Use the property of logarithms that says log_b(b^x) = x. Here, b is 4 and x is 3.
Step 7: Therefore, log_4(4^3) = 3.
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