# Aptitude - Surds and Indices - Discussion

Discussion Forum : Surds and Indices - General Questions (Q.No. 2)
2.
 If a x - 1 = b x - 3 , then the value of x is: b a
 1 2
1
2
 7 2
Explanation:

 Given a x - 1 = b x - 3 b a

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

x - 1 = 3 - x

2x = 4

x = 2.

Discussion:
26 comments Page 1 of 3.

I didn't understand for solve the method. Please explain.

Ravi kiran said:   1 decade ago
@pooja

(b/a) can be written as (a/b)^-1.

Based on this concept this problem is solved.

Can anybody tell me what is the concept through which this problem has been solved ?

I can not understand.

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

* Remember, sinplification is always solved by 2 or more fraction or number or alphabet.

:If the alphabet fraction is not equal to one anthor,we have reranged it.

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

: Then we have to take power for simplification.

= x-1= 3-x

* When the number goes after or before '=' sign the sign changes

: Now we have to change the places.

= 2x=4
=x=2

Yashi Jain said:   1 decade ago
How could you add the powers when there is an = sign between the two.

Rakesh KIIT said:   1 decade ago
(a/b)^x-1=(b/a)^x-3
can be written as :

After cross multiplication :

(a)^(2x-4)=(b)^(2x-4)
=>(a/b)^(2x-4)=1
=>(a/b)^(2x-4)=(a/b)^0
=> 2x-4=0
=>x=4/2
=>x=2

SANJIV KUMAR said:   1 decade ago
Everybody can you tell me that how cross multiplication (a)^(2x-4) = (b)^(2x-4) in this answer.

Manu said:   10 years ago
The problem can be solved by using the property "If the bases are equal then there powers must be equal". So in order to find the value we have to make the bases equal, after equating solve for x.

Faheem said:   9 years ago
Any one can explain in detail.