Question

Solve the equation without a calculator:

(logx)^2=log(x^2)

Answer 1

(logx)^2=log(x^2)
(logx)^2=2logx
(logx)^2-2logx = 0
logx (logx - 2) =0
logx =0 or logx -2 = 0 <- solve these 2 equations.

Answer 2

When it's solved it's like... why didn't I think of that, sigh.... Thanks @Callisto

Answer 3

Welcome. It's just a matter of experience.

Answer 4

\[\log(x) \times \cancel{\log(x)} = 2 \cancel {\log(x)}\]

logx = 2

Answer 5

x=1 and x=100

Answer 6

Yes you are right..

Answer 7

@waterineyes Honestly, you shouldn't cross out the variable like that, even though you can do that by putting it = 0.

Answer 8

And I guess... in reference to the experience

Answer 9

Ya I got it Callisto because the equation is quadratic and you will get two values but I am getting one..

Answer 10

@purplec16 lol It's just a trick I used in the exam

Answer 11

But I don't recommend you do that. Just stick to the way I posted. It's safer.

Answer 12

Oki, thanks once again!

Answer 13

x^2 = 2x
x^2 - 2x =0
x( x-2) =0
x=0 or x-2 =0
^^ Use this method!!


But from that you can see that
\(x^2 = 2x\)
\(x \times x = 2x \)
''Cancel'' the x
\(x=2\) or \(x=0\)

Answer 14

what happens when you take the log of a log like log(logx)

Answer 15

The value would become smaller?!

Answer 16

No I mean like log(logx)=2...

Answer 17

10^100=x?

Answer 18

or is this a cancellation?

Answer 19

log(logx)=2
logx = 10^2
logx = 100
x = 10^100

Answer 20

Yay me! I'm getting it! Thanks for your help! Your the bestest!

Answer 21

Welcome. I'm not the best though

Answer 22

Yeah you are!