Science Forums 2

[Don Blazys]

To:CraigD. In post number 13 of this thread, I wrote:

(T/T)a^x+(T/T)b^y=(T/T)c^z=

T(c/T)^((zln(c)/(ln(T))-1)/(ln(c)/(ln(T))-1)).

Factoring does not involve the cancelled variable T, and results in:

((T/T)a^(x/2))^2+((T/T)b^(y/2))^2=((T/T)c^(z/2))^2=

(T(c/T)^(((z/2)ln(c)/(ln(T))-1)/(ln(C)/(ln(T))-1)))^2.

This is algebraically correct. It is not a mistake.
Now when you wrote: "It should be:

((T/T)a^(x/2))^2+((T/T)b^(y/2))^2=((T/T)c^(z/2))^2=

T^2(c/T)^((((z/2)ln(c)/(ln(T))-1)/(ln(c)/(ln(T))-1)))2),"

you inadvertently put in an odd number of parenthesis, that is, thirteen ")", but only twelve "(".

I'm sure that this was just a "typo", and that what you really meant to write was either:

T^2(c/T)^(((z/2)ln(c)/(ln(T))-1)/(ln(c)/(ln(T))-1)2),

or:

T^2(c/T)^((zln(c)/(ln(T))-2)/(ln(c)/(ln(T))-1)),

which is exactly what we get when we remove the outermost parenthesis in my original post!

If your intent was indeed to eliminate the outermost parenthesis in my original version, then your LaTex rendering is correct, and the logarithmic exponent that you wrote, which is:

z ln(c)
------- -1
2 ln(T)
-------------- 2
ln(c)
------- -1
ln(T)

can also be written as:

zln(c)
------- -2
ln(T)
-------------
ln(c)
------- -1
ln(T)

I did not make an algebraic mistake.

Don.