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2015-04-25T12:24:32+05:30

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      25^x-1 = 5^(2x-1) - 100
⇒ 5^2x-2 = 5^(2x-1) - 100
⇒ 5^2x-2 - 5^2x-1 = -100
⇒ 5^2x [ 5^-2 - 5^-1] = - 100
⇒ 5^2x [ 1  -  1 ]  = - 100
             25    5
⇒ 5^2x [ 1 - 5]  = - 100
               25
⇒ 5^2x [ -4 ] = - 100
              25
⇒ 5^2x [-4] = -100 * 25
⇒ 5^2x = 100 * 25     [ - * - = +]
                  4 
⇒ 5^2x = 625
⇒ 5^2x  = 5^4 
so, ⇒  2x = 4
      ⇒  x = 2
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2015-04-25T16:42:53+05:30

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
We need to bring together the terms containing x.  Then constant terms on the other side.  Then simplify by performing the addition/subtraction/multiplication.

25^{x-1}=5^{2x-1}-100\\\\=>\ (5^2)^{x-1}=5^{2x-1}\ -2^2*5^2\\\\=>\ 5^{2x-2}-5^{2x-1}\ = - 2^2*5^2\\\\=>\  5^{2x-2}*[ 1-5^1 ]=-2^2*5^2\\\\=>\  5^{2x-2}*-4=-4*5^2\\\\=>\  2x-2=2\\\\x=2

done.
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