Question 1202791
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Find x if 5^(2x+1) +5^(2x)= 3750
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<pre>
Your original equation 

    {{{5^(2x+1) + 5^(2x)}}} = 3750

can be EQUIVALENTLY re-written in the form

    {{{(5)*5^(2x) + 5^(2x)}}} = 3750,

or

    {{{(6)*5^(2x)}}} = 3750.


It implies

     {{{5^(2x)}}} = {{{3750/6}}} = 625.


So, we have 

    {{{5^(2x)}}} = 625 = {{{5^4}}}.


Hence,

     2x = 4,   x = 4/2 = 2.


<U>ANSWER</U>.  x = 2.
</pre>

Solved.