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25^x - 6*5^x + 5 = 0

Let us rewrtie 25^x

We know that 25 = 5^2

==> 25^x = 5^x)^2

Then let us rewrtie the equation:

(5^x)^2 - 6*5^x) + 5 = 0

Now let us assume that 5^x = y

==> y^2 - 6y + 5 = 0

...

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25^x - 6*5^x + 5 = 0

Let us rewrtie 25^x

We know that 25 = 5^2

==> 25^x = 5^x)^2

Then let us rewrtie the equation:

(5^x)^2 - 6*5^x) + 5 = 0

Now let us assume that 5^x = y

==> y^2 - 6y + 5 = 0

Now we will factor:

==> ( y - 5)(y-1) = 0

==> y1= 5 ==>  5^x1 = 5 ==> x1 = 1

==> y2= 1 ==> 5^x2 = 1 ==> x2 = 0

Then we have two solutions:

x = { 0, 1}

Approved by eNotes Editorial Team