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

Question 979915: Solve. 625^x-4= 25^x+5
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!

What equation would you solve: this one

- = + ,

or this one

= ???

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

= .

Note that 625 = .

Therefore, you can write the original equation in the form

= .

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.

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