I can't seem to solve this:
3x = 10^-0.3x
All I do is go around in circles
Is your problem I presume,Originally Posted by freswood
$\displaystyle 3x=10^{.3x}$
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.