Question

$if \: {5}^{2x - 1} = {25}^{x - 1} + 100 .$
find the value of x.​

Answer 1

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

Answer 2

Step-by-step explanation:

Given :

${5}^{2x - 1} = {25}^{x - 1} + 100$

Find :

The value of x.

Solution :

$= > {5}^{2x - 1} = ( {5}^{2} )^{x - 1} + 100$

$= > {5}^{2x - 1} - {5}^{2x - 2} = 100$

$= > {5}^{2x - 2}. {5}^{1} - {5}^{2x - 2} = 100$

$= > {5}^{2x - 2} (5 - 1) = 100$

$= > {5}^{2x - 2} \times 4 = 100$

$= > {5}^{2x - 2} = 25$

$= > {5}^{2x - 2} = {5}^{2}$

$= > 2x - 2 = 2$

$= > 2x = 4$

$= > x = \frac{4}{2}$

$= > x = 2.$

Hence :

The value of x is 2.

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