Science Forums 2

[CraigD]

Originally Posted by Don Blazys

To: CraigD. The equation:

(T/T)a^x=T(a/T)^((xln(a)/(ln(T))-1)/(ln(a)/(ln(T))-1))

is both true and correct. It is not false!

As I trivially prove in post #2, the equation is true only for the special cases of or

The flaw with the proposed identity is that exponentiation isn’t associative with multiplication, that is .

Originally Posted by Don Blazys

You made a mistake when you put it into LaTex.

I did. My apologies – I’ve corrected it.

Since the exponent in question still equate to , however, the difference has no impact on the proof.

Originally Posted by Don Blazys

Due to circumstances beyond my control, I can't post in LaTex at this time.

No special software is needed to use the LaTeX math package in hypography posts, just the post entry box, or whatever text editor you use to make posts. Once you’ve learned a few basic functions, such as \frac{a}{b} as an equivalent of a/b, you’ll find LaTeX text it’s very similar to the text you’ve already written. For example, the LaTeX for
(T/T)a^x=T(a/T)^((xln(a)/(ln(T))-1)/(ln(a)/(ln(T))-1))
is
\left( \frac{T}{T}\right)a^x = T \left( \frac{a}{T} \right) ^{\left( \frac{\left( \frac{x \ln(a)}{\left( \ln(T)-1\right)} \right)}{\left( \frac{\ln(a)}{\left( \ln(T)-1\right)} \right)} \right)}
If the parenthesis made unnecessary by the other markups are omitted, it’s an even simpler
\frac{T}{T}a^x = T \left(\frac{a}{T} \right)^{ \frac{\frac{x \ln(a)}{\ln(T)-1}}{\frac{\ln(a)}{\ln(T)-1}} }

Originally Posted by Don Blazys

You know, when I was in high school back in the 60's, we didn't have personal computers, calculators and the like. We used pencil, paper and slide rule to solve our math problems, and although my generation developed much of the technology in use today, we never became overly dependent on it.

We didn’t have PCs when I was in high school in the ‘70s, either. Though there are some input devices that manage to make a computer fairly equivalent to paper and pencil, I, and nearly everyone I know, still use paper and pencil for most math and graphical sketching. Only when “neatening up” for posting do we transcribe into LaTeX or another computer displayable form.

An alternative to using LaTeX or similar math markup schemes is to scan paper documents and upload them as images or thumbnails in your posts. You’ll notice that members such as Turtle (who writes a lot of complicated, pretty things that can’t be rendered in LaTeX) do this quite a bit. For ordinary math expressions, however, most people find it easier to use LaTeX, especially folk who don’t have easy access to a scanner.