a) the code for the matlab function is as given below. The function has been named ''lollipop'' for generality. function log_b_x = lollipop( b , x ) % we use the given for

The log function does exactly what you want. log(14 - y) If you want a base 10 log, you use log10. There is also a log2 function, which gives a base 2 log. Other bases are achieved using the simple relation log(X)/log(b) produces a log to the base b. You could write a function for it as: logb = @(X,b) log(X)/log(b); logb(9,3) ans = 2 which is as expected. Finally, there is the reallog function, which also does the natural log, but it produces an error when the log would have been a complex number. log(-2) ans = 0.693147180559945 + 3.14159265358979i reallog(-2) Error using reallog Reallog produced complex result. But for the more normal case, reallog does the same thing as log. log(2) ans = 0.693147180559945 reallog(2) ans = 0.693147180559945

logB(X) = logA(X) / logA(B) You can pick A to be one of the built in functions, like log or log2 or log10. E.g., log3(9) = log(9) / log(3) , or log3(9) = log10(9) / log10(3) , etc.

The formula is: For any given base b, you need to compute a constant .

Probably because most other languages follow that same naming convention. Not sure why, just historical I guess.