Question

evaluate each expression $$\log _{5} 5$$

   evaluate each expression
$$\log _{5} 5$$

Precalculus

Robert Blitzer 6th Edition

Chapter 3, Problem 35

Instant Answer

Solved by Expert Nick Johnson

08/21/2021

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This is a logarithm with base 5 and the number is also 5. Show more…

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evaluate each expression $$\log _{5} 5$$

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Key Concepts

Definition of Logarithms

A logarithm is the inverse operation to exponentiation. It answers the question, 'To what exponent must a base be raised to produce a given number?' The logarithm log_b(a) represents the exponent x such that b^x = a. This concept is fundamental in many branches of mathematics, connecting exponential growth and scaling processes with their rates of change.

Identity Property of Logarithms

One of the key properties of logarithms is the identity log_b(b) = 1. This property states that the logarithm of a base taken with respect to itself is always equal to one, because any number raised to the power of one is itself (i.e., b^1 = b). This property simplifies many logarithmic expressions and is a fundamental concept in simplifying logarithmic equations.

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