Solving for Q in the equation T = Q + 2^(Q-2)

[Overflowing]

This one has me stumped. This is not homework, this is someone's attempt to estimate growth of corals in a marine aquarium. I don't know where he came up with this equation...

$$T = Q + 2^{(Q-2)}$$

 

[dacruick]

I'm not sure you can solve for Q here

 

[Overflowing]

I've been trying to figure it out with ln functions and substitution, etc...I've seen something like this before in college it seems. Some kind of transform or algorithm...just can't put my finger on it.

 

[Guffel]

The Lambert function needs to be used to express the non-trivial solutions.

http://www.wolframalpha.com/input/?i=solve+T+=+Q+++2^(Q-2)+for+Q

 

[jackmell]

$$(t-q)=2^{q-2}$$
$$(t-q)2^{2-q+t}=2^t$$
$$(t-q)2^{t-q}=2^{t-2}$$
$$\log(2)(t-q)e^{(t-q)\log(2)}=\log(2)2^{t-2}$$
$$t-q=\frac{W[2^{t-2}\log(2)]}{\log(2)}$$

$$q=t-\frac{W[2^{t-2}\log(2)]}{\log(2)}$$

 

[Overflowing]

You guys rock

Thanks!