Question 979915


What equation would you solve: this one


{{{625^x}}} - {{{4}}} = {{{25^x}}} + {{{5}}}, 


or this one


{{{625^(x-4)}}} = {{{25^(x+5)}}} ???


You can answer me in the &nbsp;&nbsp;>>>Tnanks you<<<&nbsp;&nbsp; section. 

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<B>Comment from student</B>: &nbsp;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, &nbsp;our equation is 


{{{625^(x-4)}}} = {{{25^(x+5)}}}.


Note that 625 = {{{25^2}}}. 


Therefore, &nbsp;you can write the original equation in the form


{{{25^(2(x-4))}}} = {{{25^(x+5)}}}.


It gives you the equation for exponents


2(x-4) = x + 5.


It is easy to solve. &nbsp;Simplify it step by step:


2x - 8 = x + 5,

x = 13.


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


<B>Answer</B>. &nbsp;x = 13


<B>Note</B>. &nbsp;For solving exponential equations see my lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/logarithm/How-to-solve-exponential-equations.lesson>Solving exponential equations</A>&nbsp; in this site.