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8.6 solving exponential and log equations
 

8.6 solving exponential and log equations

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    8.6 solving exponential and log equations 8.6 solving exponential and log equations Presentation Transcript

    • 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.
    • Examples: Solve:
    • Your Turn! Solve
    • Solving by Taking Logs If it is not easy/possible to rewrite using same bases, take the log (with base b) of both sides. Examples:
    • Your Turn! Solve
    • 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:
    • Example: Solve
    • Your Turn! Solve
    • Natural Base Exp. Equations Get the exponential part alone. Take the ln of each side. Example:
    • 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
    • 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?
    • Solving Log Equations For two logs with the same base: Example: Solve
    • Your Turn! Solve
    • Equations with One Log “Chop off the log” and write in exponential form. Then solve for x. Example: Solve
    • Your Turn! Solve
    • Extraneous Solutions The domains of log functions are limited. This sometimes produces extraneous solutions. Always check answers in original equation. Example: Solve
    • Example: Solve
    • Your Turn! Solve