If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form. log₅ 5 = 1

Verified step by step guidance

1. Identify the given statement: \( \log_5 5 = 1 \). This is in logarithmic form.
2. Recall the relationship between logarithmic and exponential forms: \( \log_b a = c \) is equivalent to \( b^c = a \).
3. In the given statement, the base \( b \) is 5, the result of the logarithm \( c \) is 1, and the argument \( a \) is 5.
4. Rewrite the logarithmic statement \( \log_5 5 = 1 \) in exponential form using the formula: \( 5^1 = 5 \).
5. This shows the equivalence between the logarithmic and exponential forms of the statement.

Key Concepts

Definition of Logarithms

A logarithm answers the question: to what exponent must the base be raised to produce a given number? Formally, log_b(a) = c means that b^c = a. Understanding this definition is essential to convert between logarithmic and exponential forms.

Conversion Between Exponential and Logarithmic Forms

Exponential and logarithmic forms are two ways of expressing the same relationship. The exponential form b^c = a corresponds to the logarithmic form log_b(a) = c. Recognizing this equivalence allows one to rewrite expressions from one form to the other.

Properties of Logarithms with Base and Argument

When the base and the argument of a logarithm are the same, such as log_5(5), the logarithm equals 1 because any number raised to the power 1 is itself. This property helps simplify and verify logarithmic expressions.