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Math Help - word problem using logarithms

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    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) = I_{0}(0.8)^x , where x is the thickness of the glass, in millimetres, and 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?
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    Quote Originally Posted by extraordinarymachine View Post
    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) = I_{0}(0.8)^x , where x is the thickness of the glass, in millimetres, and 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 I(x) = 0.75 \, I_0

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

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

    Solve for x
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