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Solving Exponential Equations

Equations with terms raised to exponents including x

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Exponential Equations

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Logarithms are simply another tool that can be used to isolate a variable when solving for x.  It is important to remember that when a log of a side of an equation is taken, the entire side is put inside the log function.  For example, taking the log of 3x+5y = 12 would result in log(3x+5y) = log(12), not log(3x)+log(5y) = log(12).  Also remember that logs do not "cancel out" an exponent's base unless the base of the log and the exponent match.  More tips are listed below.

Tips

Utilize the addition/subtraction log rules: they can be used to combine to log terms

Not only can you take the log of both sides, but you can also put a number to the power of each side and maintain equality. (e.g. 2x = 6, 32x = 36).

Utilize the exponent rule to "bring down" variables (e.g. log(32x) = 2x•log(3))

If the log's base and the exponent's base DO match, then they will drop out (e.g. log(104)=4)

Practice problems can be found here.

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