Question

If 5^(2x-1) = 25^(x-1) + 100, find the value of 3^(1+x).

Answer 1

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
then x=2
we have find 3^(x+1)
x=2
3^(x+1)=x^3+1+3x^2+3x
=x(x^2+1)+3x(x+1)
=(x^2+1)(3x+x)

Answer 2

hope it is helpful for you

please mark me as brainliest