SOLUTION: Find x if 5^(2x+1) +5^(2x)= 3750

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Question 1202791: Find x if 5^(2x+1) +5^(2x)= 3750
Found 2 solutions by ikleyn, mananth:
Answer by ikleyn(53763) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find x if 5^(2x+1) +5^(2x)= 3750
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Your original equation 

    5%5E%282x%2B1%29+%2B+5%5E%282x%29 = 3750

can be EQUIVALENTLY re-written in the form

    %285%29%2A5%5E%282x%29+%2B+5%5E%282x%29 = 3750,

or

    %286%29%2A5%5E%282x%29 = 3750.


It implies

     5%5E%282x%29 = 3750%2F6 = 625.


So, we have 

    5%5E%282x%29 = 625 = 5%5E4.


Hence,

     2x = 4,   x = 4/2 = 2.


ANSWER.  x = 2.

Solved.



Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
Find x if 5^(2x+1) +5^(2x)= 3750
5%5E%282x%2B1%29+%2B5%5E%282x%29=+3750

5%5E%282x%2B1%29+=+5%5E%282x%29+%2A+5%5E1+ (a^m*a^n= a^(m+n)
we get
5*5^(2x) +5^(2x)= 3750

5^(2x)*(5+1) 3750
5^2x = 3750/5 = 625
5^(2x) = 5^4= 5^(2*2)
Base same compare indices
2x=4
x=2