[tex]if \: {5}^{2x – 1} = {25}^{x – 1} + 100 .[/tex]
find the value of x.​

2 thoughts on “<br />[tex]if \: {5}^{2x – 1} = {25}^{x – 1} + 100 .[/tex]<br />find the value of x.​”

1. Step-by-step explanation:

   Given :

   [tex] {5}^{2x – 1} = {25}^{x – 1} + 100[/tex]

   Find :

   The value of x.

   Solution :

   [tex] = > {5}^{2x – 1} = ( {5}^{2} )^{x – 1} + 100[/tex]

   [tex] = > {5}^{2x – 1} – {5}^{2x – 2} = 100[/tex]

   [tex] = > {5}^{2x – 2}. {5}^{1} – {5}^{2x – 2} = 100[/tex]

   [tex] = > {5}^{2x – 2} (5 – 1) = 100[/tex]

   [tex] = > {5}^{2x – 2} \times 4 = 100[/tex]

   [tex] = > {5}^{2x – 2} = 25[/tex]

   [tex] = > {5}^{2x – 2} = {5}^{2} [/tex]

   [tex] = > 2x – 2 = 2[/tex]

   [tex] = > 2x = 4[/tex]

   [tex] = > x = \frac{4}{2} [/tex]

   [tex] = > x = 2.[/tex]

   Hence :

   The value of x is 2.

   Brainly Question number :

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2. 2x−2=52x−1−100

   shift 52x−2 to the left hand side

   Now, Multiply the equation with -1

   52x−1−52x−2=100

   52x−2(5−1)=100

   52x−2=4100

   25x−1=25 ( ∵ 52x−2=(52)x−1)

   now,

   x−1=1

   x=2

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