Question

If a=10^xand b=10^y and a^yb^x=100 prove that xy=1

Answer 1

Answer:

Given

a=10^x ........(1)

b=10^y.........(2)

(a^y)(b^x)==100 .....(3)

Substitute 1 and 2 in equation 3

(10^xy)(10^xy)==100

we will get 100 if the powers of the 10 in the the equation is equal to 1

so

xy=1

hence the proof