Evaluate log of 1

Problem

(log_)(1)

Solution

1. Identify the base of the logarithm. In most contexts, (log_)() without a specified base refers to the common logarithm (base 10) or the natural logarithm (base e.

2. Apply the property of logarithms which states that the logarithm of 1 in any valid base b is always 0.

3. Recall the definition of a logarithm: (log_b)(x)=y is equivalent to by=x

4. Substitute the values into the definition: since b0=1 for any b>0 and b≠1 it follows that (log_b)(1)=0

Final Answer

(log_)(1)=0

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