# Thread: word problem using logarithms

1. ## word problem using logarithms

Hi, i need help please on how to set up this question, and how to solve it. Thanks!

The intensity, I, of light, in lumens, passing through the glass of a pair of sunglasses is given by the equation I(x) = $\displaystyle I_{0}(0.8)^x$ , where x is the thickness of the glass, in millimetres, and $\displaystyle I_{0}$ is the intensity of the light entering the glasses. How thick should the glass be so that it will block 25% of the light entering the sunglasses?

2. Originally Posted by extraordinarymachine
Hi, i need help please on how to set up this question, and how to solve it. Thanks!

The intensity, I, of light, in lumens, passing through the glass of a pair of sunglasses is given by the equation I(x) = $\displaystyle I_{0}(0.8)^x$ , where x is the thickness of the glass, in millimetres, and $\displaystyle I_{0}$ is the intensity of the light entering the glasses. How thick should the glass be so that it will block 25% of the light entering the sunglasses?
To block 25% of light means to let 75% through so $\displaystyle I(x) = 0.75 \, I_0$

$\displaystyle \frac{0.75 \, I_0}{I_0} = 0.8^x$

$\displaystyle ln(0.75) = x\, ln(0.8)$

Solve for x