SOLUTION: solve. 8^2x-3 =1/16

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Question 816712: solve. 8^2x-3 =1/16
Found 2 solutions by ewatrrr, MathTherapy:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

The idea is to try to find the same base on both sides of the EQ

8%5E%282x-3%29+=+1%2F16****

8%5E%282x-3%29+=+16%5E%28-1%29

8%5E%282x-3%29+=+%288%5E%284%2F3%29%29%5E%28-1%29

8%5E%282x-3%29+=+%288%5E%28-4%2F3%29%29

  2x-3 = -4/3

 6x-9 = -4

  6x = 5

   x = 5/6

CHECKING our answer***

 8%5E%285%2F3-+9%2F3%29+=+8%5E%28-4%2F3%29+=+1%2F16

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

solve. 8^2x-3 =1/16 


8%5E%282x+-+3%29+=+1%2F16

%282%5E3%29%5E%282x+-+3%29+=+2%5E-+4 ----- Converting to base 2

2%5E%283%282x+-+3%29%29+=+2%5E-+4

2%5E%286x+-+9%29+=+2%5E-+4

6x - 9 = - 4 ----- Bases are equal and so are their exponents

6x = 5

highlight_green%28x+=+5%2F6%29

You can do the check!! 



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