# 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 |

Answer: Option

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*

2*x* = 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.

=>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

I am not getting this. Please help me to understand better.

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

x = 2 is answer.

(a/b)^-(x-3).

Let compare thier powers;

x - 1 = -(x - 3).

x - 1 = -x + 3

x + x = 1 + 3.

2x = 4

x = 2 is answer.

(1)

AkshI gori said:
7 years ago

Not understanding it. Please help me to get it.

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

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

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