Questions: Evaluate log base 1/2 of 1.

Transcript text: Evaluate $\log _{1 / 2} 1$.

Solution

Solution Steps

To evaluate $\log_{1/2} 1$, we need to determine the power to which the base $1/2$ must be raised to yield the number 1. By definition, any non-zero number raised to the power of 0 is 1. Therefore, $\log_{1/2} 1 = 0$.

Step 1: Understanding the Logarithm

To evaluate $\log_{1/2} 1$, we need to find the exponent $x$ such that $\left(\frac{1}{2}\right)^x = 1$.

Step 2: Applying the Definition of Logarithm

By the properties of exponents, we know that any non-zero number raised to the power of 0 equals 1. Therefore, we can conclude that: \[ \left(\frac{1}{2}\right)^0 = 1 \]

Step 3: Conclusion

Thus, we find that: \[ \log_{1/2} 1 = 0 \]

Final Answer

$\boxed{0}$

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