SOLUTION: Solve for x: 5 to the power of 2x+3 minus 5 to the power of 2x = 3100 Please show steps, thanks!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve for x: 5 to the power of 2x+3 minus 5 to the power of 2x = 3100 Please show steps, thanks!      Log On


   

Question 133331: Solve for x: 5 to the power of 2x+3 minus 5 to the power of 2x = 3100
Please show steps, thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5%5E%282x%2B3%29-5%5E%282x%29+=+3100 Start with the given equation


5%5E%282x%29%2A5%5E%283%29-5%5E%282x%29+=+3100 Break up 5%5E%282x%2B3%29 to get 5%5E%282x%29%2A5%5E%283%29. Remember, x%5E%28y%2Bz%29=x%5Ey%2Ax%5Ez


5%5E%282x%29%285%5E%283%29-1%29+=+3100 Factor out the common term 5%5E%282x%29



5%5E%282x%29%28125-1%29+=+3100 Evaluate 5%5E3 to get 125


5%5E%282x%29%28124%29+=+3100 Subtract


5%5E%282x%29+=+25 Divide both sides by 124


5%5E%282x%29+=+5%5E2 Rewrite 25 as 5%5E2


Since the bases are equal, this means that the exponents are equal

So 2x=2


x=1 Divide both sides by 2 to isolate x


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Answer:
So the solution is x=1