Log circuit op-amp

EC.24)Identify the op-amp circuit above and define the relationship between the input and output voltage ,given the diode-current voltage :$i_D =I_S(e^{[qv_D/kT]} -1)$.Here, $I_S$is a constant dependent on diode construction.
q is electron charge
k is Boltzmann's constant
T is absolute temperature.
Then,v_i at the input equals
(a)$-RI_S(e^{[qv_o/kT]} -1)$
(b)$-RI_S(e^{[-qv_o/kT]} +1)$
(c)$R/I_S(e^{[qv_o/kT]})$
(d)insufficient data,cannot be determined

Answer is (a)

The voltage at inverting input can be neglected such that the output voltage equals the diode voltage.Under this condition, $i_D$ and $i_R$ sum to zero i.e., $i_D + i_R = 0 ,\implies i_R=-i_D$
$i_R = v_i/R, \implies v_i = -Ri_D$
$\therefore v_i = -RI_S(e^{[qv_D/kT]} -1)$