Question

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Q56⟩⟩ If $\sf{\bigg(\dfrac{a}{b}\bigg)^{x-1}=\bigg(\dfrac{b}{a}\bigg)^{x-3}}$, then x equals?​

Answer 1

Answer:

2 is the answer.

Step-by-step explanation:

HOPE THIS HELPS.

Answer 2

Step-by-step explanation:

Given :-

(a/b)^(x-1) = (b/a)^(x-3)

To find :-

Find the value of x ?

Solution :-

Given equation is (a/b)^(x-1 )= (b/a)^(x-3)

It can be written as

=> (a/b)^(x-1) = 1/(a/b)^(x-3)

=> (a/b)^(x-1 )= (a/b)^-(x-3)

Since a^-n = 1/a^n

the bases are equal

=> The exponents must be equal

=> x-1 = -(x-3)

=> x-1 = -x+3

=> x+x = 3+1

=> 2x = 4

=> x = 4/2

=> x = 2

Therefore, x = 2

Answer:-

The value of x for the given problem is 2

Check:-

If x = 2 then

LHS = (a/b)^(x-1)

=>(a/b)^(2-1)

=> (a/b)^1

=>(a/b)------(1)

RHS =(b/a)^(x-3)

=>(b/a)^(2-3)

=> (b/a)^-1

=>1/(b/a)

Since a^-n = 1/a^n

=> (a/b) -----(2)

From (1)&(2)

LHS = RHS is true for x = 2

Verified the given relation.

Used formulae:-

• a^-n = 1/a^n

• 1/(a/b)=b/a