Write a function that estimates the natural logarithm of a number with an error less than a specified error tolerance. Error of the estimated value is calculated as the absolute value of the difference between the estimated value and the actual value (see help logto calculate the actual value). Have the user input a number x such that 0 < x < 10 and an error tolerance. Include error handling to make sure that the user inputs a number in the specified range and provide guidance to the user to explain the appropriate range. Pass the number and error tolerance as input arguments to a function that calculates the natural logarithm for the number using the following Taylor Series explanation:

Researchers measured the data speeds for a particular smartphone carrier at 50 airports. the highest speed measured was 78.1 mbps. the complete list of 50 data speeds has a mean of x overbarequals16.11 mbps and a standard deviation of sequals18.65 mbps. a. what is the difference between carrier's highest data speed and the mean of all 50 data speeds? b. how many standard deviations is that [the difference found in part (a)]? c. convert the carrier's highest data speed to a z score. d. if we consider data speeds that convert to z scores between minus2 and 2 to be neither significantly low nor significantly high, is the carrier's highest data speed significant? a. the difference is nothing mbps.