Find x if (2/9) to the power of 5 X (9/2) to the power of -4 = [(2/9) to the power of 3] to the power of 2x multiplied by (9/2) to the power of -3
THIS SUM SAYS THE ANSWER IS 1
GIVE THE CORRECT ANSWER AS 1 AND EXPLAIN THE STEPS CLEARLY.
I WILL MARK YOU AS BRAINLIST FOR SURE.
Answers
Step-by-step explanation:
Given :-
(2/9)^5 ×(9/2)^-4 =[ (2/9)^3]^2x × (9/2)^-3
To find :-
Find the value of x ?
Solution:-
Given equation is
(2/9)^5 ×(9/2)^-4 =[ (2/9)^3]^2x × (9/2)^-3
On taking LHS
=> (2/9)^5 ×(9/2)^-4
=> (2/9)^5 × (2/9)^4
Since a^-n = 1/a^n
=> (2/9)^(5+4)
Since a^m × a^n = a^(m+n)
=> (2/9)^9
LHS = (2/9)^9 ---------(1)
On taking RHS
[(2/9)^3]^2x × (9/2)^-3
=> (2/9)^(3×2x) × (9/2)^-3
Since (a^m)^n = a^(mn)
=> (2/9)^6x × (9/2)^-3
=> (2/9)^6x × (2/9)^3
Since a^-n = 1/a^n
=> (2/9)^(6x+3)
Since a^m × a^n = a^(m+n)
=>RHS = (2/9)^(6x+3)------------(2)
From (1)&(2)
(2/9)^9 = (2/9)^(6x+3)
Since the bases are equal then exponents must be equal
=> 9 = 6x+3
=> 6x+3 = 9
=> 6x = 9-3
=> 6x = 6
=>x = 6/6
=> x = 1
Therefore, x = 1
Answer:-
The value of x for the given problem is 1
Check:-
LHS
=> (2/9)^5 ×(9/2)^-4
=> (2/9)^5 × (2/9)^4
=> (2/9)^(5+4)
=> (2/9)^9
LHS = (2/9)^9 ---------(1)
If x = 1 then RHS
[(2/9)^3]^2x × (9/2)^-3
=> [(2/9)^3]^2 × (9/2)^-3
=> (2/9)^6 × (2/9)^3
=> (2/9)^(6+3)
RHS = (2/9)^9 ---------(2)
From (1)&(2)
LHS = RHS is true for x = 1
Verified the given relations in the given problem.
Used formulae:-
- a^m × a^n = a^(m+n)
- a^-n = 1/a^n
- If the bases are equal then exponents must be equal
only fine not so good