Question

in each of the following find the value of x​

Answer 1

Answer:

iii)x=6

iv)x=2/3

Step-by-step explanation:

just get the basics right

Answer 2

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