Aptitude - Surds and Indices - Discussion

Discussion :: Surds and Indices - General Questions (Q.No.2)

2. 

If a x - 1 = b x - 3 , then the value of x is:
b a

[A].
1
2
[B]. 1
[C]. 2
[D].
7
2

Answer: Option C

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.


Pooja said: (Sep 26, 2010)  
I didn't understand for solve the method. Please explain.

Ravi Kiran said: (Oct 18, 2011)  
@pooja

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

Based on this concept this problem is solved.

Nem Prasad said: (Dec 8, 2011)  
Can anybody tell me what is the concept through which this problem has been solved ?

Basavaraju said: (Jan 20, 2012)  
I can not understand.

Nisikanta said: (May 31, 2012)  
(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: (Jun 9, 2012)  
How could you add the powers when there is an = sign between the two.

Rakesh Kiit said: (Sep 2, 2012)  
(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: (Jul 9, 2014)  
Everybody can you tell me that how cross multiplication (a)^(2x-4) = (b)^(2x-4) in this answer.

Manu said: (Feb 11, 2015)  
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: (Mar 26, 2015)  
Any one can explain in detail.

Yammu said: (Feb 7, 2016)  
If (b/a) reciprocal how will power gets negative?

Akshi Gori said: (Jun 25, 2016)  
Not understanding it. Please help me to get it.

Husain Sr said: (Aug 25, 2016)  
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.

Lawal Adetunji said: (Apr 25, 2017)  
I am not getting this. Please help me to understand better.

Heman said: (Jun 23, 2017)  
(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.

Priya said: (Jun 26, 2017)  
I am not understanding this method. Please explain me in detail.

Sachin D said: (Jul 7, 2017)  
Thanks @Heman.

Priyadharshini said: (Jul 29, 2017)  
I can understand very easily. Thank you @Heman.

Hemz said: (Sep 12, 2017)  
Thanks @Heman.

Shweta said: (Jan 8, 2018)  
@Husain.

When you compare the power then , x-1=-x-3.
Then how you change the sign of ,x-1=x+3?

Panther said: (Mar 10, 2018)  
How come 4?

Ashish said: (May 20, 2018)  
I am not geting. How to solve this?

Frazer Juma said: (Nov 20, 2019)  
Thanks, guys! I understood very well.

Suryateja said: (Jun 2, 2020)  
Am not getting this, please explain in detail.

Urvashi said: (Jul 22, 2020)  
Simply Cross Multiply them a with a and b with b.

It becomes;

[a ^(x-1) ][a^(x-3)] = [b^(x-1)][b^(x-3)].
Power will get add on both sides.
Then,
a^(2x-4) = b^(2x-4),
Simply, x=2.

Yesubabu said: (May 30, 2021)  
@Urvashi.

You are absolutely right, Thanks for explaining.

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