Check out some similar questions!

LynnM · Sep 2, 2010, 01:14 PM

Hi. The question says to solve logx^{2} = (logx)^{2}.

My brain tells me to do this:

10^{logx^{2}} = 10^{logx} * 10^{logx}

x^{2} = x * x

x = x

The text solution says that my brain is mistaken and the answer should be 1 or 0. Not too sure how to get that. I can see that they working by plugging them into the original equation but I can't figure out how to come up with them as answers.

Unknown008 · Sep 3, 2010, 08:58 AM

Lol, okay, let's try again.

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

As I see it, it's not this easy to solve... so, let's make use of a substitution, that is, let:

$y = log x$

So? We first find all the log x.

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

$2 log x = (logx)(logx)$

Now, let's use y = log x.

$2y = y^2$

Can you solve for y now? Once you get that, replace y again by log x. This time, you should get the answer. Post what you do! :)

LynnM · Sep 3, 2010, 09:40 AM

Okay, I've got it! Here it goes:

$2y=y^2$

$0=y^2-2y$

$0=y(y-2)$

so... logx=0 and logx-2=0...

$10^{logx}=10^0$

$x=1$

and...

$10^{logx}=10^2$

$x=100$

yay!:)