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. 3^4 = 81

Verified step by step guidance

1. Identify the given form: The statement is in exponential form, which is \(3^4 = 81\).
2. Recall the relationship between exponential and logarithmic forms: If \(a^b = c\), then the equivalent logarithmic form is \(\log_a{c} = b\).
3. Apply the relationship to the given statement: Here, \(a = 3\), \(b = 4\), and \(c = 81\).
4. Write the equivalent logarithmic form: \(\log_3{81} = 4\).
5. Verify the conversion: Check that the base, exponent, and result are correctly placed in the logarithmic form.

Key Concepts

Exponential Form

Exponential form expresses a number as a base raised to a power, indicating how many times the base is multiplied by itself. For example, in the expression 3^4, 3 is the base and 4 is the exponent, meaning 3 is multiplied by itself four times, resulting in 81.

Logarithmic Form

Logarithmic form is the inverse of exponential form and expresses the exponent needed to achieve a certain value from a base. For instance, the logarithmic form of 3^4 = 81 is log3(81) = 4, indicating that 4 is the exponent to which the base 3 must be raised to yield 81.

Conversion Between Forms

Converting between exponential and logarithmic forms is a fundamental skill in algebra. The general relationship is that if a^b = c, then loga(c) = b. This conversion allows for solving equations and understanding the relationship between bases, exponents, and their results.