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8-4 Properties of Logarithms Check Skills You’ll Need Page 446 Properties of Logarithms PRODUCT QUOTIENT POWER log b MN log b M log b N M log b log b M log b N N x log b M x log b M Loudness of Sounds Decibels I L 10 log I0 I is the intensity of the sound wave in watts per square meter. I0 is the lowest-intensity sound that the average human ear can detect. Noise Control L1 = present loudness L2 =reduced loudness I1 = present intensity L1 – L2 is how much the loudness changed. I2 = reduced intensity I1 I2 L1 L2 10 log 10 log I0 I0 8-5 Exponential and Logarithmic Equations Taking the log of both sides of an equation. Change of Base formula. If an equation is in exponential form, then take the log of both sides. If an equation is in logarithmic form, then write it in exponential form. Don’t forget to use the properties. Intentionally blank 8-6 Natural Logarithms Remember e. The function y = ex has an inverse, THE NATURAL LOGARITHMIC FUNCTION. ye x log e y x ln y x Properties All of the properties of common logarithms apply to natural logarithms also.