Question

Solve each logarithmic equation. Express all solutions in exact form.

log x^2= (log x)^2

Answer 1

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

2* log(x) = (log x)^2

2 = log(x)

// now i just reverse the two sides

log(x) = 2

x = e^2

Answer 2

the answer is 1100.

Answer 3

just don't know how???

Answer 4

well if it is as you typed it above, then x is not 1100. check this out

http://www.wolframalpha.com/input/?i=log+x%5E2%3D+%28log+x%29%5E2

Answer 5

\[\log_{} x ^{2}=(\log_{}x) ^{2}\]
that's how the question looks in my book

Answer 6

one rule of logs is

log(x^n) = n*log(x)

Answer 7

Ok I'll try that. Thank you.

Answer 8

Tomo, you missed a solution by canceling. You need to factor and set each of the factors equal to zero.

Answer 9

actually i made a mistake that @Hoa caught.

i was thinking in terms of natural log which is why I used e^2. since we are using base 10 we should actually have

x = 10^2 = 100

Answer 10

http://www.wolframalpha.com/input/?i=log+x%5E2%3D+%28log+x%29%5E2&a=*FunClash.log-_*Log10.Log-

Answer 11

Wait, so I write it like
\[10^{logx ^{2}}=10^{(logx)^{2}}\]

Answer 12

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

2* log(x) = (log x)^2

2 = log(x)

we have log base 10.

10^2 = x

Answer 13

Thats not corect. You are missing a solution
(log(x))^2-2log(x)=0
(log(x))(log(x)-2)=0
log(x)=0 and log(x)=2

Answer 14

true, that log(x) =0 is missing

log(x) = 0

10^0 = x

x = 1

AND

log(x) = 2

10^2 = x

x = 100

Answer 15

@Xavier it is not "not corect" just miss one solution.

Answer 16

But why does the answer in the book say {1,100}?

Answer 17

@joshuaknmcguire that means the solution is 1 and 100

Answer 18

The procedure there where log(x) is cancelled from both sides is bad.

Answer 19

sorry, or not and

Answer 20

OOOOOOOOOOOOH shoot sorry guys!!!! AHH

Answer 21

aye aye aye I thought it was eleven hundred

Answer 22

hihihi....

Answer 23

learn from mistake . good. by the way. Xavier is the best way.

Answer 24

Thank you @Hoa , @Xavier , and @tomo

Answer 25

you're welcome