Transcript of "8.6 solving exponential and log equations"
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Solving Exponential Equations If two powers with the same base are equal, then their exponents must be equal. To solve using this property: Rewrite equation so the bases match. Set exponents equal to each other. Solve for x.
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More Examples: Taking Logs Not all equations will be that basic! Must get the exponential part by itself, first. Then, take the log of both sides. Last, continue solving for x. Example:
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Natural Base Exp. Equations Get the exponential part alone. Take the ln of each side. Example:
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Exponential Models Newton’s Law of Cooling – the temperature T of a cooling substance is modeled by where: t = time (in minutes) T0 = initial temp. of substance TR = room temp. r = cooling rate
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Example: Your mom is making soup for dinner. When she takes it off the stove, it is 212ºF. The room temp. is 70ºF and the cooling rate of the soup is r = 0.046. How long will you have to wait to eat the soup at a safe temp. of 100ºF?
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Solving Log Equations For two logs with the same base: Example: Solve
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Extraneous Solutions The domains of log functions are limited. This sometimes produces extraneous solutions. Always check answers in original equation. Example: Solve
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