Simple mathematical problem

by Mechatron
Tags: ellen, equation, exp(), math, mathematical, simple
 P: 38 Is this equation equal to: (e^(hf/kT)) - 1 or e^( (hf/kT) - 1 ) http://s29.postimg.org/le6iqy3rb/exp.png
 P: 237 The former.
Mentor
P: 21,311
 Quote by Mechatron Is this equation equal to: (e^(hf/kT)) - 1 or e^( (hf/kT) - 1 ) http://s29.postimg.org/le6iqy3rb/exp.png
First off, what you wrote is NOT an equation. An equation always has an = symbol in it.

The image in the link is [exp(hf/kT) - 1].

What you have written is ambiguous, as what you probably meant is this:
$$e^{\frac{hf}{kT} - 1}$$

What you actually wrote, though, is this:
$$e^{\frac{hf}{k}T - 1}$$

The brackets - [] - around the entire expression are unnecessary.

PF Gold
P: 1,355
Simple mathematical problem

 Quote by Mark44 First off, what you wrote is NOT an equation. An equation always has an = symbol in it. The image in the link is [exp(hf/kT) - 1]. What you have written is ambiguous, as what you probably meant is this: $$e^{\frac{hf}{kT} - 1}$$ What you actually wrote, though, is this: $$e^{\frac{hf}{k}T - 1}$$ The brackets - [] - around the entire expression are unnecessary.
Why did you put the -1 in the exponential? The parenthesis limit the argument of exp to hf/kT.

My guess is that Mechatron did not write that himself, but saw it in a book. It's most probably related to the Planck distribution (blackbody radiation). As economicsnerd said, the correct reading is
$$e^{\beta h f} - 1 \mbox{ where } \beta = \frac{1}{kT}$$
The additional bracket [] might be there because it is part of a greater equation.
 P: 4 Im sorry to be off topic but I'm using a i device and i can't see (what i think to be) mathematical symbols that are in this thread... They appear as dollar signs and other randoms, i was wondering if maybe I'm short of additional download or setting adjustments. All help is highly appreciated
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P: 21,311
 Quote by DrClaude Why did you put the -1 in the exponential? The parenthesis limit the argument of exp to hf/kT.
The posted image, which doesn't have the -1 term, doesn't match the expressions in the first post. In the first post Mechatron asks about these expressions:
(e^(hf/kT)) - 1

and

e^( (hf/kT) - 1 )

In any case, this is moot, as Mechatron has been banned from PF.

 Quote by DrClaude My guess is that Mechatron did not write that himself, but saw it in a book. It's most probably related to the Planck distribution (blackbody radiation). As economicsnerd said, the correct reading is $$e^{\beta h f} - 1 \mbox{ where } \beta = \frac{1}{kT}$$ The additional bracket [] might be there because it is part of a greater equation.

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