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. 3⁴ = 81

Verified step by step guidance

1. Identify the components of the exponential equation \$3^4 = 81$. Here, the base is 3, the exponent (or power) is 4, and the result is 81.
2. Recall the relationship between exponential and logarithmic forms: an exponential equation \(a^b = c\) can be rewritten as a logarithmic equation \(\log_a c = b\), where \(a\) is the base, \(b\) is the exponent, and \(c\) is the result.
3. Apply this relationship to the given equation by setting the base of the logarithm to 3, the argument to 81, and the result to 4.
4. Write the equivalent logarithmic form as \(\log_3 81 = 4\).
5. This expresses the original exponential statement in logarithmic form, showing that the logarithm base 3 of 81 equals 4.

Key Concepts

Exponential Form

Exponential form expresses a number as a base raised to an exponent, such as a^b = c, where 'a' is the base, 'b' is the exponent, and 'c' is the result. It shows repeated multiplication of the base.

Logarithmic Form

Logarithmic form is the inverse of exponential form and is written as log_base(result) = exponent. It answers the question: 'To what power must the base be raised to get the result?'

Conversion Between Exponential and Logarithmic Forms

Converting between forms involves rewriting a^b = c as log_a(c) = b, and vice versa. This conversion helps solve equations and understand relationships between exponents and logarithms.