SOLUTION: Solve. 625^x-4= 25^x+5

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Question 979915: Solve. 625^x-4= 25^x+5
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!

What equation would you solve: this one

625%5Ex - 4 = 25%5Ex + 5,

or this one

625%5E%28x-4%29 = 25%5E%28x%2B5%29 ???

You can answer me in the   >>>Tnanks you<<<   section.
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Comment from student:  The 2nd one you mentioned is what i'm looking for with x-4 being a whole exponent and the x+5 being an exponent.
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OK.

So,  our equation is

625%5E%28x-4%29 = 25%5E%28x%2B5%29.

Note that 625 = 25%5E2.

Therefore,  you can write the original equation in the form

25%5E%282%28x-4%29%29 = 25%5E%28x%2B5%29.

It gives you the equation for exponents

2(x-4) = x + 5.

It is easy to solve.  Simplify it step by step:

2x - 8 = x + 5,
x = 13.

Indeed,  2(x-4) = 2(13-4) = 2*9 = 18,  and  x + 5 = 13 + 5 = 18.

Answer.  x = 13

Note.  For solving exponential equations see my lesson  Solving exponential equations  in this site.