Final answer:
The question requires knowledge of the natural logarithm function, which is the inverse of the exponential function, specifically demonstrating that ln(20) = x represents the power to which Euler's number must be raised to get 20, and relates to understanding exponential growth.
Step-by-step explanation:
The question 'Write the given logarithmic equals ln20=x' is asking to express the natural logarithm of 20 as a variable. In mathematics, the logarithmic function and the exponential function are inverses of each other. This means that the expression ln(ex) is equal to x, and eln(x) is equal to x. Therefore, when given ln(20) = x, it's understood that x is the power to which e (Euler's number, approximately 2.718) must be raised to produce 20.
Moreover, this concept is fundamental in understanding exponential growth and decay in various fields such as economics, biology, and physics. For instance, a growth rate of 2.3% corresponds to a natural logarithm of 10 being approximately 2.30, revealing the connection between logarithms and percentage growth rates. Lastly, logarithmic properties such as log(a) - log(b) = log(a/b) shows how simple subtraction can represent division in a logarithmic scale, which is reflected in logarithmic graphs where the same vertical distance indicates the same ratio of change, regardless of the actual size of the values involved.