Alpha in Economics equation

K^alpha

how to find alpha if not given?

is it K/TFC or K/Y?

I think alpha will be given under the terme: cost of capital per total factor cost or labor share of total factor cost. If not given, it can be calculated from this equation at equilibrium: g_Y (1-alpha) = g_T

Algebra:

Y = TK_α_L(1α)

log(Y) = log(TK_αL(1−α)) = log(T) + log(Kα_) + log(L(1−α)) = log(T) + _α_log(K) + (1 − α)log(L)

log(Y) − log(T) = _α_log(K) + log(L) − _α_log(L)

log(Y) − log(T) − log(L) = α[log(K) − log(L)]

α = [log(Y) − log(T) − log(L)] / [log(K) − log(L)]