# Logarithmic Word Problem

• Jan 10th 2010, 11:04 PM
Marko_02
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)
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Solve the equation of I(d)
• Jan 10th 2010, 11:31 PM
pickslides
I am going to assume the base of your log is 'e'

Therefore

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

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

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

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