Question

Answer 1

Script: naturallog.m

x = input("\nEnter the x value to determine the natural log (0 to 2): ");
prec = input("Enter the precision for natural log : ");

fprintf("-----------------------------\n");

if x <= 0 || x >= 2.0
fprintf("Error! Natural log must be greater than 0 and less than or equal to 2\n");
else
x = 1.0 * x;
prec = 1.0 * prec;

term = 1;
sign = 1;
sum = 0;
diff = prec + 1;

while diff > prec
    sum += sign * ((x-1.0) ^ term)/term;
    fprintf("\nTerm %d: Current value of Natural Log series is %f", term, sum);
    term += 1;
    diff = abs(sum - log(x));
    sign = -1 * sign;
end

fprintf("\n\nActual ln(%f) = %f", x, log(x));
fprintf("\nSeries ln(%f) = %f", x, sum);
fprintf("\n%d terms required to acheive a precision of %f\n", term-1, prec);
end

Execution and Output:

naturallog Enter the x value to determine the natural log (θ to 2): 1.125 Enter the precision for natural log : .θ8801 Term 1: Current value of Natural Log series is 0.125000 Term 2: Current value of Natural Log series is θ. 117188 Term 3: Current value of Natural Log series is 0.117839 Term 4: Current value of Natural Log series is θ. 117778 Actual ln (1.125000)0.117783 Series ln (1.125000)0.117778 4 terms required to acheive a precision of θ .000010 naturallog Enter the x value to determine the natural log (θ to 2): 1.125 Enter the precision for natural log : 1 Term 1: Current value of Natural Log series is 0.125000 Actual ln (1.125000)0.117783 series in (1.125000 ) -0.125000 1 terms required to acheive a precision of 1.000000 naturallog Enter the x value to determine the natural log (θ to 2): θ Enter the precision for natural log : .01 Error! Natural log must be greater than θ and less than or equal to 2