Final answer:
To convert the exponential equation 3^4 = 81 into logarithmic form, it becomes log_3(81) = 4, demonstrating that exponential and logarithmic functions are inverses.
Step-by-step explanation:
To write the exponential equation 34 = 81 as a logarithm, you would express it in the form of a logarithmic equation. In logarithmic form, the base of the exponential (which is 3) becomes the base of the logarithm, the exponent (which is 4) becomes the value of the logarithm, and the result of the exponential equation (which is 81) becomes the input to the logarithmic function.
Therefore, the equivalent logarithmic equation is log3(81) = 4.
This transformation is based on the understanding that the exponential function and the logarithmic function are inverses of each other. In general, if ab = c, then loga(c) = b.
The logarithm of a number raised to an exponent is indeed the product of the exponent and the logarithm of the number.