Express 2 lg 3√x - lg 4/3x^2 + log(100)4x^3 in the form a lg x + lg b ,where a and b are constants .

Answer 1

assuming log(100) means log base 100,
and assuming 4/3x^2 means 4/(3x^2),

2 lg 3√x - lg 4/3x^2 + log(100)4x^3
lg 9x - lg 4/3x^2 + 1/2 lg 4x^3
lg 9 + lg x - lg 4 + lg 3 + 2lg x + lg 2 + 3/2 lg x
(1+2+3/2)lg x + lg(9/4*3*2)
9/2 lg x + lg 27/2