Solve the simultaneous equations : 1/4 Ω x = 4 3 Ω 2x = y 請幫忙, 謝謝?

Not too sure if the symbol Ω is meant to be exponent ^.

Following solution assumes the equation to be:

(1/4)^x=4(3^(2x))=y

If it is not the case, you can solve in a similar way.

First solve

(1/4)^x=4(3^(2x))

take (natural) log on both sides

x*log(1/2)=(2x)*log(3)+log(4)

isolate x:

x(log(1/2)-2log(3))=log(4)

x=log(4)/(log(1/2)-2log(3))

Evaluating right-hand side,

x=-0.3868528 approx.

check: (1/4)^x-4(3^(2x))=0, ok.

hence

y=(1/4)^x=(1/4)^-0.3868528=1.70966 approx.