Question

Solve for this

Answer 1

\[\log _{2}(x^2-2x)=3\]

a) -2,4 b)-2 c)4

Answer 2

use the definition of log,
\(\Large \log_ab=c \implies b = a^c\)

so what about
\(\log_2(x^2-2x)=3 \implies ??\)

Answer 3

Hey there, I know the answer myself it's a)-2,4 but my teacher marked it wrong so im wondering if my answer is right or wrong.

Answer 4

I know that x^2-2x=8 and move it over giving somethign like (x+2)(x-4) and I got 2 answers but I dont know if it's both.....

Answer 5

we can verify by plugging in the values we got in the original equation

Answer 6

so, plug in x = -2 first,
in original equation, what u get on left ?

Answer 7

Yes and I did, it worked but my teacher marked me wrong simply because in her theory, anything with logs, x can't be smaller than 0

Answer 8

both worked.

Answer 9

Is that true?

Answer 10

true.
both are actually the solution of your equation.

Answer 11

Yes, but she marked me wrong because x shouldn't be bigger than 0.... I dont understand....

Answer 12

smaller*

Answer 13

x can surely be smaller than 0

the quantity under log |....| cannot be 0

Answer 14

if there's log a, then a needs to be positive.

Answer 15

I've argued that and she denied it wtf.....

Answer 16

I told her that and she's like nope... I even graphed it for her....

Answer 17

so, in your case, you're getting x^2-2x as positive which is valid.
you're correct. your teacher is wrong.

Answer 18

Oh god, I'm gonna drop that class now thanks dude...

Answer 19

lol, don't drop it :P logs are interesting :) forget about this small incident :P

Answer 20

It's affecting my grade really harshly... I'm gonna take adult ed for math if I can get consent from my counselor...

Answer 21

good luck anyways! :)

Answer 22

Alright man..

Answer 23

thanks for doing this for me.

Answer 24

you're welcome ^_^