Is my teacher wrong??

[azure linden]

By the way,

My answer was: (m-n)^2
Correct answer was: 2(m-n)

[normal glacier]

Your teacher is wrong

I bet they misinterpreted $\log_{4}\left(1.6\right)^{2}$ as $\log_{4}\left(1.6^{2}\right)$

[remote fox]

BlockLayer2000

[normal glacier]

The value of $\log_{4}\left(1.6\right)$ is definitely $m-n$, so the value of $\left(\log_
{4}\left(1.6\right)\right)^{2}$ is $\left(m-n\right)^{2}$

[remote fox]

BlockLayer2000

[azure linden]

I showed her exactly that but on a graphing calculator and she said that's because of how they format it on calculators, but when writing it you can omit the brackets from the log. I said you can't because it just creates ambiguity and she just vehemently denied it.

[normal glacier]

What? Most people would assume $\log_{4}\left(1.6\right)^{2}=\left(\log
_{4}\left(1.6\right)\right)^{2}$

[remote fox]

BlockLayer2000

[azure linden]

she 100% didn't confuse it, it was an actual test that goes towards our grade, not just a randomly handed out practice test. It was made and checked over by the whole math department which is insane to me how this got every teacher's approval.

[azure linden]

I swear to god i wrote this exact thing down saying that's what the question is implying and she said that's not the same thing

[normal glacier]

v

Wolfram agrees with you

v

Geogebra agrees with you

I can't think of any other calculators

[azure linden]

well the thing is she said when the square is there, it's on the argument and that to square the whole log, it has to be written like this which makes no sense because when the square is there, is it implying the whole thing is squared? I said to move the 2 down it must be log((1.6)^2) or log(1.6^2) and she said no

[normal glacier]

well clearly the top three most respected math calculators disagree

[azure linden]

this is where im sort of seeking consultation because i swear shes just flat out wrong

[normal glacier]

Yeah, if you try to input that expression on geogebra is literally auto-formats to what you're saying

[normal glacier]

I think you should ask them to change the test for the future to put the squared in parens

[azure linden]

Alright ill show her on monday when i see her next. Thank you 🙏

[azure linden]

yeah they ain't gonna listen

😭

[normal glacier]

My argument is, the teachers are arguing that their interpretation is the only correct one, but every calculator says that your interpretation is the correct one, so you should be marked correctly.

Sorry about that

[normal glacier]

If the goal was for you to evaluate $\log_{4}\left(1.6^{2}\right)$, then they shouldn't have a problem moving the parens. And if their goal was also to make you interpret $\log_{4}\left(1.6\right)^{2}$ as $\log_{4}\left(1.6^{2}\right)$, then that's when they should see literally evaluating those expressions give different results

[remote fox]

BlockLayer2000