1. ## indicial equation

I can't seem to solve this:

3x = 10^-0.3x

All I do is go around in circles

2. Originally Posted by freswood
I can't seem to solve this:

3x = 10^-0.3x

All I do is go around in circles
$\displaystyle 3x=10^{.3x}$
Let, $\displaystyle y=.3x$
Then,
$\displaystyle 10y=3x$
Thus,
$\displaystyle 10y=10^{y}$
Thus,
$\displaystyle y=10^{y-1}$
We can see that $\displaystyle y=1$ is a solution because,
$\displaystyle 1=10^{1-1}=10^0=1$
Thus,
$\displaystyle .3x=1$
thus,
$\displaystyle x=\frac{10}{3}$
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Though I did not prove it, I believe there are no other solutions because this leads to the Lambert function, but I do not know if this is a high school problem or a problem for Analysis class which your professor want to demonstrate with the Lambert function. If a high school function igonore this entire paragraph.

3. Ta heaps.

Ugh why didn't I think of that?? I can be such an idiot sometimes.

4. Originally Posted by freswood
Ugh why didn't I think of that??
Maybe because you do not pay attention is class but fool around with you palm pilot and play games

5. Originally Posted by ThePerfectHacker
Maybe because you do not pay attention is class but fool around with you palm pilot and play games

Maybe it's because I'm not a very lateral thinker and this is the best I can do

6. Originally Posted by ThePerfectHacker
$\displaystyle 3x=10^{.3x}$
Let, $\displaystyle y=.3x$

[snip]

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Though I did not prove it, I believe there are no other solutions because this leads to the Lambert function, but I do not know if this is a high school problem or a problem for Analysis class which your professor want to demonstrate with the Lambert function. If a high school function igonore this entire paragraph.

the function:

$\displaystyle f(x)=10^{0.3x}-3x$

is increasing on $\displaystyle (-\infty,\infty)$ so any real root will be unique.

RonL

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# simple indical equations

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