How to differentiate logarithms with the ti 89?

Question

I'm having difficulty entering the the correct syntax into my ti 89 calculator to differentiate logarithms.

So far this is what I cam up with for f'(X) = log6(x^2-3x-4) 1. f3 click differentiate 2. catalog click log( 3. enter syntax log(6)(x^2-3x-4),x)

correct answer is (2x-3)/(x^2-3x-4)*(ln6)

I do not return that answer with my syntax please help! And thank you

Answer 1

On the TI-89 Titanium, you could take the base $b$ log of $x$ by entering log(x,b) into the calculator.

In this case, type in d(log(x^2-3x-4,6),x) and you should get the right answer. The d needs to be the special character differentiation d (see this page, or the calculator's manual, for more details). Everything else can be typed in directly from the keyboard: you can, if you like, type in log( by pressing [♦] [7], but it's also okay to just type it in letter by letter.

On the regular TI-89, log(x,b) is not allowed, and there's no feature that allows logs to arbitrary bases, but you can replace it by ln(x)/ln(b). So you'd type in d(ln(x^2-3x-4)/ln(6),x) and otherwise proceed as above. (Using log(x)/log(b) would also work.)