sum help please and thanks

1^x = 1/2

xlog(1) = log 1/2

x * 0 = log 1/2

no solution

This post was edited by zackill4 on Sep 20 2013 02:52pm

1^x = (1/2)

take log base 1 of both sides:

(log base 1) 1^x = (log base 1) (1/2)

log base 1 of 1 cancels, leaving x on the left side:

x = (log base 1) (1/2)

then change of base:

x = [ln 1/2]/[ln 1]

don't have a calculator on hand, as far as i can take it. just plug and chug

Yeah, I just posted that.. and the problem is that ln(1) = 0, since you must raise a number to the 0th power to get one (unless it's one).

Edit: A more intuitive answer is that 1 raised to any power is 1, so yeah... can't get 1/2

This post was edited by zackill4 on Sep 20 2013 02:57pm

do you mean square root of one?
then the result would be +1 and -1
or
do you want the solution of the equation 1^x=1/2?
sorry, there is no solution

That contains a subtle mistake:

As brmv and zackill4 have said:



Or a hand waving argument:
I send 3 people to the lumber yard, I give them the instructions:
"Bring me back a board that is Logbase 1 of 1 feet long."

The first guy says, hmmm well 1^6 = 1, and decides to bring me a 6 foot board.

The second guy say, hmmm well 1^300 = 1, and brings back a 300 foot board.

The third guy is a mathematician and says to himself: 1^0 = 1, and so comes back with a 0 foot board (or no board at all).

They all 3 followed the instructions but came back with very different board lengths. Clearly the expression is not defined well.

clearly we can not simplify logbase1(1)^x in that manor.

This post was edited by Azrad on Sep 20 2013 05:12pm