hi people
pls answer my question.
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Answers
Step-by-step explanation:
4)
Given that :
(16)^0.16 × (16)^0.04 × (2)^0.2
16 = 2×2×2×2 = 2^4
It can be written as
=> (2^4)^0.16 × (2^4)^0.04 × (2)^0.2
=> (2)^(4×0.16) × (2)^(4×0.04) × (2)^0.2
Since (a^m)^n = a^(mn)
=>(2)^0.64 × (2)^0.16 × (2)^0.2
=> 2^(0.64+0.16+0.2)
Since a^m × a^n = a^(m+n)
=> (2)^1.0
=> 2^1
=> 2
The value of (16)^0.16 × (16)^0.04 × (2)^0.2 is 2
5)
Given equation is (4/11)^(x-1) = (11/4)^(x-5)
=> (11/4)^(1-x) = (11/4)^(x-5)
Since a^-n = 1/a^n
and
Since the bases are equal then exponents must be equal.
=> 1-x = x-5
=> 1+5 = x+x
=> 6 = 2x
=> 2x = 6
=> x = 6/2
=> x = 3
The value of x = 3
Answer :-
4) The value of (16)^0.16 × (16)^0.04 × (2)^0.2 is 2
5) The value of x for the given problem is 3
Check :-
5) If x = 3 then LHS of the equation is
(4/11)^(3-1)
=> (4/11)^2
=> 16/121
RHS = (11/4)^(3-5)
=> (11/4)^-2
=> 1/(11/4)^2
=> (4/11)^2
=> 16/121
LHS = RHS is true for x = 3
Used formulae:-
- (a^m)^n = a^(mn)
- a^-n = 1/a^n
- a^m × a^n = a^(m+n)
- If the bases are equal then exponents must be equal.