in each of the following find the value of x
Answers
Answer:
iii)x=6
iv)x=2/3
Step-by-step explanation:
just get the basics right
Step-by-step explanation:
Given :-
(3^-2×4^-2)^-3 = 12^x
(1/3)^-2 + (1/4)^-2 = 125^x
To find :-
Find the value of x ?
Solution :-
I)
Given that (3^-2×4^-2)^-3 = 12^x
=> [(3×4)^-2]^-3 = 12^x
Since a^m × b^m = (ab)^m
=> (12^-2)^-3 = 12^x
=> 12^(-2×-3) = 12^x
Since (a^m)^n = a^mn
=> 12^6= 12^x
=>6 = x
Since the bases are equal then exponents must be equal
Therefore,x = 6
ii)
Given that :(1/3)^-2 + (1/4)^-2 = 125^x
=> [1/(1/3)]²+[1/+1/4)]² = 125^x
Since a^-n = 1/a^n
=> (3)²+(4)² = 125^x
=> (3×3)+(4×4) = 125^x
=> 9+16 = 125^x
=>25 = 125^x
=> 5² =( 5³)^x
=> 5² = 5^(3x)
Since (a^m)^n = a^mn
=> 2 = 3x
Since the bases are equal then exponents must be equal
=>3x = 2
=> x = 2/3
Therefore,x = 2/3
Answer:-
I) The value of x for the given problem is 6
ii) The value of x for the given problem is 2/3
Used formulae:-
- a^m × b^m = (ab)^m
- (a^m)^n = a^mn
- a^-n = 1/a^n
- If the bases are equal then exponents must be equal