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.

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! :)

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!:)