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Chapter 2: Problem 1

\(\log _{a} 1\) is equal to (a) 0 (b) 1 (c) \(\infty\) (d) 10

Short Answer

Expert verified
The correct answer is (a) 0.

Step by step solution

01

Understanding the properties of logarithms

Recall the property that any number (except 0) raised to the power of 0 gives the result of 1. This can be written as \(a^0 = 1\). We can see here that 'a' is the base and '0' is the exponent.
02

Apply the property of logarithms to the exercise

We can transfer the above relationship \(a^0 = 1\) into logarithmic form using the definition of a logarithm. The logarithm base 'a' of 1 is equal to the exponent which a must be raised to produce 1. In this case, the exponent is 0. Therefore, the expression \(\log _{a} 1\) equals 0.

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