A firm's revenue function from the sale of $21 is R(x) = 2x2 - 9x-221 and the firm's total cost function is given by C(x) = x2 +4 where x represents the level

Ques 4) 2^(3x-1)=1/16 Taking log on both sides, (3x-1)ln(2)=ln(1/16) 3x-1=ln(1/16)/ln⁡(2)=-4 x=-1 4^x-2^x-12=0 2^2x-2^x-12=0 Let 2^x=y y^2-y-12=0 y^2-4y+3y-12=0 y(y-4)+3(y-4)=0 (y-4)(y+3)=0 y=4,-3 As 2^x can’t be negative 2^x=4 Taking log on both sides, xln(2)=ln⁡(4) xln(2)=2 ln⁡(2) x=2 y=3×2^x y=3×2^x y=2^(-x) Equating, 2^(-x)=3×2^x 2^(-2x)=3 Taking log on both sides, -2xln(2)=ln⁡(3) x=ln⁡(3)/(-2 ln⁡(2) )=-0.792 y=2^(-(-0.792))=1.732 P (-0.792, 1.732) 1+2〖log〗_5 x=〖log〗_5 (16x-3) 〖log〗_5 5+〖log〗_5 x^2=〖log〗_5 (16x-3) 〖log〗_5 〖5x〗^2=〖log〗_5 (16x-3) 5x^2=16x-3 5x^2-16x+3=0 x=(16±√((-16)^2-4(5)(3) ))/2(5) =(16±√196)/10=(16±14)/10=1/5,3 x=0.2,3