Question

If 25−1 = 5

2−1

, then find x.


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Answer 1

5 2x−2 =5 2x−1 −100

shift 5

2x−2 to the left hand side

Now, Multiply the equation with -1

5 2x−1 −5 2x−2 =100

5 2x−2

(5−1)=10

5 2x−2 = 4100

25 x−1 =25

( ∵ 5

2x−2 =(5 2 )

x−1

)

now,

x−1=1

x=2

Answer 2

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25^(x -1 ) = 5^(2x - 1) - 100

=> 5^2(x-1)=5^(2x-1) -100

=> 5^(2x-2 ) = 5^(2x-1) -100.

(5^2x)/25=(5^2x)/5 - 100

(5^2x)(1/25–1/5)=-100

(5^2x)(-4/25)=-100

(5^2x)=100×25/4= 25×25=5^4

Equating exponents on both sides, we get

=> 2x = 4

=> x=4/2=2. Answer.