Problem 36 - Introductory and Intermediate Algebra for College Students 4th

Question

Evaluate each expression without using a calculator. $$\log _{11} 11$$

Step-by-Step Solution

Answer

1

Step 1: Understanding the properties of logarithms

A fundamental property of logarithms states that if \( \log _{a} a = 1 \) for any positive number \( a \). This is because any number raised to the power of 1 gives the number itself.

Step 2: Apply the property to our problem

Using the property above, we can say that \( \log _{11} 11 = 1 \) because 11 to the power of 1 gives 11.

Step 3: Conclusion

So the expression \( \log _{11} 11 \) simplifies to 1.