# 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 2 of 3.

Priya said:   6 years ago
I am not understanding this method. Please explain me in detail.

Heman said:   6 years ago
(a/b)^x-1=(b/a)x-3.
=>a^x/b^1=a^-3/b^-x,
=>a/b^x-1=a/b^3-x,
=>x-1=3-1,
=>x=2.

Lawal Adetunji said:   7 years ago

Husain SR said:   7 years ago
Here (a/b)^x-1 and (b/a)^x-3 now if we reciprocal b/a to a/b then there is negative sign on it.
(a/b)^-(x-3).

Let compare thier powers;

x - 1 = -(x - 3).
x - 1 = -x + 3
x + x = 1 + 3.
2x = 4
(1)

AkshI gori said:   7 years ago

Yammu said:   8 years ago
If (b/a) reciprocal how will power gets negative?

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

Manu said:   9 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.

SANJIV KUMAR said:   9 years ago
Everybody can you tell me that how cross multiplication (a)^(2x-4) = (b)^(2x-4) in this answer.

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