Problem 36
Question
Evaluate each expression without using a calculator. $$\log _{11} 11$$
Step-by-Step Solution
Verified Answer
The value of the expression \( \log_{11} {11} \) is 1.
1Step 1: Recognize properties of logarithms
The logarithm of a number in the same base is always equal to 1. This is because the logarithm of a number x to the base b is the power to which we must raise b to obtain x. In this case, we have \( \log_{11} {11} \). Here, the base and the number are the same, which means that the power to which we must raise 11 to get 11 is just 1.
2Step 2: Simplify the expression
So, \( \log_{11} {11} = 1 \). Hence, the value of the given expression is 1 without using a calculator.
Other exercises in this chapter
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