Question

Modulus and log

Answer 1

\[\huge \left| x-3 \right|^{3x^2-10x+3}=1\]

Answer 2

Tried taking log both sides?

Answer 3

right hand sde would become 0

Answer 4

\(3x^2 - 10x + 3 \log |x-3| = 0\)

Answer 5

Yeah, RHS will become 0.

Using power rule, the power of |x-3| will come out of the log as multiplication.

\((3x^2 - 10x + 3) \log |x-3| = 0\)

Answer 6

So, you have two cases

\[ \left\{
\begin{array}{lr}
3x^2 - 10x + 3 = 0\\
\log |x-3| = 0
\end{array}
\right.
\]

Answer 7

the first one can be solved

Answer 8

\(\cfrac{10 \pm \sqrt{100 - 36}}{6} = \cfrac{10 \pm 8 }{6} = 3 ~~ \text{or} ~~\cfrac{1}{3} \)

So, x = 3 or 1/3 for the given function to be zero.

Now, for \(\log |x-3| = 0 \)

There are again two cases.

Answer 9

how does log of moduluses work

Answer 10

Squaring both sides will work I think.

Answer 11

No. that will not work.

Answer 12

1st case :-
log(x-3) =0
x-3=1
x=4

2nd case
-log(x-3)=0
dividing by -1
log(x-3)=0
x-3=1
x=4

Answer 13

b^(x-3)=3n
for any b>1

Answer 14

When x is real then

\(\log |x-3| = \cfrac{1}{2} \log (x-3)^2 = 0 \)

Thus, \(\log (x-3)^2 = 0\)

Answer 15

What's wrong with the above method

Answer 16

As \(\log (x-3)^2 = 0\)

Therefore, \( (x-3)^2 = 1\)

Thus, x-3 = 1 or x-3 = -1

x = 4 or x = 2

Answer 17

Why did you square , and what's wrong with the method i did

Answer 18

The method I did followed the properties of logarithms.

You can follow this method -

log|x-3| = 0

|x-3| = 1

(x-3) = - 1 or (x-3) = 1

x = 2 and x = 4

For your method

(x-3) = +1 or (x-3) = -1

Answer 19

\(\color{blue}{\text{Originally Posted by}}\) @No.name

2nd case
-log(x-3)=0
dividing by -1
log(x-3)=0
\(\bf{x-3=1} \)
x=4
\(\color{blue}{\text{End of Quote}}\)

The bolded text has the problem... you only took one condition which is x-3 can also be equal to (-1)

Answer 20

3 won't be the solution

Answer 21

* which is x-3 = 1 but (x-3) can also be equal to -1

Answer 22

Yeah i did some goof up there but you got the point.
I am already a bit frustated as my internet is not working

Answer 23

That's modern generation... ^ We all are depended on internet.... ! When it doesn't work, we get frustrated hahahah ... ! Have fun.

Answer 24

make sure to check all the solution you get, by plugging them into original equation, and checking whether left side = right side.
you will find that x= 3 is not a solution

Answer 25

I wonder how my parents did engineering without internet
yes @hartnn

Answer 26

Oh yes.. 3 wouldn't be a soln

@hartnn - you got a point.. gr8

Answer 27

If there was no google / wiki -> all would have been playing out door games and having fun with friends RATHER THAN playing video games ...

all would have been going to their friends/teachers to ask questions RATHER THAN openstudy..

Answer 28

* no internet (not google/wiki :P )

Answer 29

wiki is not reliable!!!

Answer 30

Its not a reliable source, anyone can edit on it... so when looking for info you've always gotta look at other resources to ensure the info is valid.

Answer 31

Nothing is reliable then...! What say?

Answer 32

Animals are reliable, many full of love, true in their affections, predictable in their actions, grateful and loyal. Difficult standards for people to live up to. =)

Answer 33

if only animals can solve math :P

Answer 34

lol

Answer 35

Humans are also animals... lol! WILD ANIMALS

(btw, this is getting off-topic, lets discuss it in chats)

Answer 36

No, last time I saw a lion solving Integral problem @hartnn ... he was almost there, hitting his heads hard at the ground ...

Answer 37

We have no reliable guarantee that the afterlife will be any less exasperating than this one, have we?

Answer 38

I once caught 2 stray kittens and tied rope around each one and gave one to my brother and we had kitten fights

Answer 39

Animals can't solve modulus and logarithms

Answer 40

You all are newbs.\[a^b = 1\]means\[a = 1\]and for all other cases\[b = 0\]

Answer 41

yessss elephants are one of the most intelligent animals around! :P

Answer 42

So \(|x - 3| =1\) and for all other cases, \(3x^2 - 10x + 3 = 0\).

No goofing up.

Answer 43

parth, we got same thing by solving

Answer 44

yeah just look at ganeshie8

Answer 45

Kewl.

Answer 46

Why log though?

Answer 47

because steps carry marks

Answer 48

LOL

Answer 49

Finally, my BSNL net worked ahaha