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how do you find a missing exponent?

3125=5^e

 Nov 1, 2014
 #1
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If the variable is in an exponent, find the log (or ln) of both sides:

log(3125)  =  log(5^e)              With logs, exponents come out as multipliers:

log(3125)  = e x log(5)

log(3125) / log(5)  =  e     --->     e  = 5

If you haven't had logs, think of it this way:

Is 3125 some power of 5?     Not 1, 2, 3, or 4;  but 5^5  =  3125.

Since 3125 = 5^5,  e must be 5.

 Nov 1, 2014

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