Question

If x=10^a, y=10^b and (x^b*y^a) ^c=100 then prove abc =1​

Answer 1

Step-by-step explanation:

x=10^a → x^1/a=10

y=10^b. → y^1/b=10

Therefore, x^1/a = y^1/b → x=y^a/b

Given,

(x^b*y^a)^c=100

[ (y^a/b)^b*y^a]^c=10²

(y^a*y^a)^c=10²

(y^a+a)^c=10²

(y^2a)^c=10²

y^2ac=10²

(10^b)^2ac=10². {Since y=10^b}

10^2abc=10²

2abc=2

abc=2÷2

abc=1

Hence proved.