find the value of x: (2/7)^-2x+1 ÷ (2/7)^-3 = [(2/7)^-1]^-5
Answers
Step-by-step explanation:
Given :-
(2/7)^-2x+1 ÷ (2/7)^-3 = [(2/7)^-1]^-5
To find :-
Find the value of x ?
Solution :-
Given that
(2/7)^-2x+1 ÷ (2/7)^-3 = [(2/7)^-1]^-5
We know that
a^m / a^n = a^(m-n)
=> (2/7)^[-2x+1-(-3)] = [(2/7)^-1]^-5
=> (2/7)^(-2x+1+3) = [(2/7)^-1]^-5
=> (2/7)^(-2x+4) = [(2/7)^-1]^-5
We know that
(a^m)^n = a^(mn)
=> (2/7)^(-2x+4) = (2/7)^(-1×-5)
=> (2/7)^(-2x+4) = (2/7)^5
Since the bases are equal then exponents must be equal
=> -2x+4 = 5
=> -2x = 5-4
=> -2x = 1
=> x = 1/-2
=> x = -1/2
Therefore, x = -1/2
Answer:-
The value of x for the given problem is -1/2
Check :-
If x = -1/2 then LHS
=> (2/7)^-2x+1 ÷ (2/7)^-3
=> (2/7)^(-2×(-1/2)+1)÷(2/7)^-3
=> (2/7)^(1+1)÷(2/7)^-3
=> (2/7)^2 ÷(2/7)^-3
=> (2/7)^(2+3)
=> (2/7)^5
and
[(2/7)^-1]^-5
=> (2/7)^(-1×-5)
=> (2/7)^5
=> RHS
LHS = RHS
Used formulae:-
→ a^m / a^n = a^(m-n)
→ (a^m)^n = a^(mn)
Step-by-step explanation:
Solution :
Given that
(2/7)^-2x+1 ÷(2/7)^-3 = [(2/7)^-1]^-5
We know that
a^m / a^n = a^(m-n)
=> (2/7)^[-2x+1-(-3)] = [(2/7)^-1]^-5
=> (2/7)^(-2x+1+3) = [(2/7)^-1]^-5 => (2/7)^(-2x+4)= [(2/7)^-1]^-5
We know that
(a^m)^n = a^(mn)
=> (2/7)^(-2x+4) = (2/7)^(-1×-5)
=> (2/7)^(-2x+4)= (2/7)^5
Since the bases are equal then exponents must be equal
=> -2x+4 = 5
=> -2x = 5-4
=> -2x = 1
=> x = 1/-2
=> x = -1/2
Therefore, x = -1/2
Answer:
The value of x for the given problem is -1/2