SOLUTION: (5^x) (5^x-1)=10

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Question 1031012: (5^x) (5^x-1)=10
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
%285%5Ex%29%285%5Ex-1%29=10

5%5E%282x%29-5%5Ex=10

5%5E%282x%29-5%5Ex-10=0

Let 5%5Ex=u
Then 5%5E%282x%29=u%5E2

Substitute u%5E2 for 5%5E%282u%29 and u for 5%5Ex

 
u%5E2-u-10=0

u+=+%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29+ 

u+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A%281%29%2A%28-10%29+%29%29%2F%282%2A1%29+ 

u+=+%281+%2B-+sqrt%281%2B40+%29%29%2F2+

u+=+%281+%2B-+sqrt%2841%29%29%2F2+

Substitute 5%5Ex for u

5%5Ex+=+%281+%2B-+sqrt%2841%29%29%2F2

Ignore the minus sign because 5x is positive:

Take the natural logarithm of both sides

ln%285%5Ex%29+=+ln%28%281+%2B+sqrt%2841%29%29%2F2%29

x%2Aln%285%29+=+ln%28%281+%2B+sqrt%2841%29%29%2F2%29
 
x+=+ln%28%281+%2B-+sqrt%2841%29%29%2F2%29%2Fln%285%29

x+=+0.813175155554523, approximately.

Edwin