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

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.