Questions: log2(1/4) - log3(1)

Transcript text: $\log _{2} \frac{1}{4}-\log _{3} 1$

Solution

Solution Steps

To solve the expression $\log_{2} \frac{1}{4} - \log_{3} 1$, we can use the properties of logarithms. The first term, $\log_{2} \frac{1}{4}$, can be simplified using the property $\log_{b} \frac{1}{a} = -\log_{b} a$. The second term, $\log_{3} 1$, is zero because any logarithm of 1 is zero. Therefore, the expression simplifies to $-\log_{2} 4$.

Step 1: Simplifying the Logarithmic Expression

We start with the expression $ \log_{2} \frac{1}{4} - \log_{3} 1 $. Using the property of logarithms, we can rewrite $ \log_{2} \frac{1}{4} $ as: \[ \log_{2} \frac{1}{4} = -\log_{2} 4 \] Since $ \log_{3} 1 = 0 $, the expression simplifies to: \[ -\log_{2} 4 - 0 = -\log_{2} 4 \]

Step 2: Evaluating $ \log_{2} 4 $

Next, we evaluate $ \log_{2} 4 $. Since $ 4 = 2^2 $, we have: \[ \log_{2} 4 = 2 \] Thus, substituting this back into our expression gives: \[ -\log_{2} 4 = -2 \]

Final Answer

The final result of the expression $ \log_{2} \frac{1}{4} - \log_{3} 1 $ is: \[ \boxed{-2} \]

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