Please, Let me know this approximation

Question

$$ N_v = 0.5(t^{2}+2t^{6/7})\ln(1+2t^{-8/7})-t^{6/7} \tag{1} $$ $$ N_v =(0.871+0.125\ln t)^2 \tag{2}$$ Eq(2) is the approximated version of Eq(1). Does anyone know how to derive (2) from (1)? I'd appreciate your intuiton.

Answer 1

The two formulas are pretty close (within about .03) for $t$ in an interval from about $.0002$ to $0.54$. But there doesn't seem to be any obvious sense in which the second is a best approximation of the first.