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Chapter 4: Problem 35

Evaluate each expression without using a calculator. $$\log _{5} 5$$

Short Answer

Expert verified
The value of the expression \(\log_5 5\) is 1.

Step by step solution

01

Understand the Logarithm Definition

A logarithm, usually written as \(\log_b a\), transforms from an exponential form to a logarithmic form. It basically asks the question: to what power should we raise the base (b) to get a? So when the base and the value are equal, the result is 1, as any number raised to the power of 1 gives itself.
02

Apply the Logarithm Definition

Following the definition, we can apply it to \(\log_5 5\). Here, base \(b\) is 5 and \(a\) is also 5. We have to find to what power we need to raise 5 (base) to get 5. Any number raised to the power of 1 is itself, therefore, \(5^1 = 5\), so the answer here will be 1.

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