logarithms Seeing Structure in Expressions

ln(5) – ln(4) = ln

ln(5) – ln(4) = ln

Thanks, Jack!

5 replies on “ln(5) – ln(4) = ln”

Surprised that this path did not lead to ln (1) = 0
Could it be that the 1 disappeared because it does not appear when it is a coefficient for a variable term?

@Michael Pershan: that seems right to me. Would not be surprised to find the same mistake with trig functions (e.g., sin(45) – sin(44) = sin(1) = sin . . . possibly for the reason that @mrdardy proposes – a false analogy to dropping 1 as a coefficient (and as an exponent).

Then, we can get cos(a) – cos(a) = cos(0) = cos

Of course, I have a bad habit of writing trig identities without arguments when I’m rushing: sin/cos = tan, etc.

Sorry to be a year late, but the feedback shown (simple red Xs) is perfect, because the student gave no opportunity for feedback on (or partial credit for) the individual steps done mentally. But I would also ask them to drop by (or address everyone if the pattern is common) and then discussion how, as tempting as it is for many of us to jump to the answer, doing so kinda breaks the system. 🙂 You can pitch them on the two wins of showing work (more feedback/credit and, hey, when putting the steps they will catch more mistakes themselves) or you can have them use my software. 🙂 They can jump to the answer, learn it is wrong, try another answer, try just one step, whatever floats their boat.

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