Final answer:
The equation e³=y in logarithmic form is expressed as ln(y) = 3, indicating that the power to which e must be raised to obtain y is 3.
Step-by-step explanation:
To express the equation e³=y in logarithmic form, we apply the principle that the logarithm of a number is the exponent to which the base must be raised to yield that number. In this case, we are dealing with the natural logarithm, where the base is the mathematical constant e (approximately 2.7182818).
According to the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number, and recognizing that e and the natural logarithm function ln are inverse functions, we can rewrite the given expression in logarithmic form as:
ln(y) = 3
This equation states that the natural logarithm of y is equal to 3; in other words, the power to which e must be raised to get y is 3.