2 Log(X) + Log 0.1 = Log 5 + Log 2

a a a a

i got X= 10 , and -10

i think all answers accepted because there is power 2 in 2 Log(X)so -10 won't be refused

is that right????

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- Jun 23rd 2012, 05:56 AMmido22log problem
2 Log(X) + Log 0.1 = Log 5 + Log 2

a a a a

i got X= 10 , and -10

i think all answers accepted because there is power 2 in 2 Log(X)so -10 won't be refused

is that right???? - Jun 23rd 2012, 06:01 AMjohnnylam123Re: log problem
2 Log(X) + Log 0.1 = Log 5 + Log 2

2logx = log (10/0.1)

2logx = log100

2logx = 2

logx=1

x=10.

x cannot be -10 ,cause logy, y<0 ,is undefined - Jun 23rd 2012, 06:03 AMjohnnylam123Re: log problem
note log is a function that have unique sol only if there is

- Jun 23rd 2012, 06:09 AMmido22Re: log problem
- Jun 23rd 2012, 06:28 AMmattoRe: log problem
x=-10 would fail the original equation.

- Jun 23rd 2012, 06:29 AMmfbRe: log problem
2Log X = Log X^2 is a formula for positive x only.

In general, $\displaystyle n\, log(|x|) = log(|x|^n)$

With complex numbers, you can evaluate log(-10) (it is a complex number), but you cannot use the formula given above, as -10 is not [real and] positive. - Jun 23rd 2012, 06:45 AMPlatoRe: log problem
- Jun 23rd 2012, 07:59 AMmido22Re: log problem
- Jun 23rd 2012, 08:18 AMPlatoRe: log problem
**What brackets?**

Are you talking parenthesis, $\displaystyle (~)~?$.

If you are you need to know that it is incorrect to write $\displaystyle \color{red}\log_a X$.

That is function notation. Just as we write $\displaystyle f(x)$, we also write $\displaystyle \log_a( X).$ - Jun 23rd 2012, 10:12 AMjohnnylam123Re: log problem
even it is loga, results is the same