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log⁡(16)log⁡(4)\frac{\log(16)}{\log(4)}

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Quotient property of logarithmsright chevron icon

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Q. log⁡(16)log⁡(4)\frac{\log(16)}{\log(4)}
  1. Recognizing Power of 44: We recognize that 1616 is a power of 44, specifically 44 squared.\newlineCalculation: 16=42 16 = 4^2 \newlineMath error check:
  2. Using Change of Base Formula: We can use the change of base formula for logarithms, which states that log⁡(a)log⁡(b)=log⁡b(a) \frac{\log(a)}{\log(b)} = \log_b(a) .\newlineCalculation: log⁡(16)log⁡(4)=log⁡4(16) \frac{\log(16)}{\log(4)} = \log_4(16) \newlineMath error check:
  3. Substituting in Logarithm: Now we substitute 1616 with 42 4^2 in the logarithm.\newlineCalculation: log⁡4(42) \log_4(4^2) \newlineMath error check:
  4. Simplifying Expression: Using the property of logarithms that log⁡b(bx)=x \log_b(b^x) = x , we can simplify the expression.\newlineCalculation: log⁡4(42)=2 \log_4(4^2) = 2 \newlineMath error check:

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