SOLUTION: find the value of a if 7^a - 7^a-5 = 117642 sqrt 7

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Question 1186981: find the value of a if 7^a - 7^a-5 = 117642 sqrt 7
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
find the value of a if 7^a - 7^(a-5) = 117642 sqrt 7
~~~~~~~~~~~~~~~~~~ 

The starting equation

     = 


is EQUIVALENT to

     = ,

       = ,


and then, canceling the common factor  16806 in both sides

     = .


It implies  

    a - 5 = ,


hence

    a = 5 +  = 6  = 6.5.    ANSWER

Solved.



Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!




Factor out 7a



Divide both sides by 71/2

















Multiply through by 16807



Divide both sides by 16806



Take logs (base 10) of both sides













Edwin
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