Question 133342
{{{5^(2x+3)-5^(2x) = 3100}}} Start with the given equation 



{{{5^(2x)*5^(3)-5^(2x) = 3100}}} Break up {{{5^(2x+3)}}} to get {{{5^(2x)*5^(3)}}}. Remember, {{{x^(y+z)=x^y*x^z}}}



{{{5^(2x)(5^(3)-1) = 3100}}} Factor out the common term {{{5^(2x)}}}




{{{5^(2x)(125-1) = 3100}}} Evaluate {{{5^3}}} to get 125



{{{5^(2x)(124) = 3100}}} Subtract



{{{5^(2x) = 25}}} Divide both sides by 124



{{{5^(2x) = 5^2}}} Rewrite {{{25}}} as {{{5^2}}}



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}}}