# Math Help - Logarithmic Word Problem

1. ## Logarithmic Word Problem

Driving in a fog at night greatly reduces the intensity of light from an approaching car. The relationship betweent the distance, d, in metres, that your car is from the approaching car and the intensity of the light, I(d), in lumens (lm), at a distance d , is given by d= -166.67 log I(d)
---------------------------------------------------------------------------------------------------------a 125

Solve the equation of I(d)

2. I am going to assume the base of your log is 'e'

Therefore

$d = -166.67 \log_e(I(d))$

$\frac{d}{-166.67}= \log_e(I(d))$

$e^{\frac{d}{-166.67}}= I(d)$

$I(d) = e^{\frac{d}{-166.67}}$