Question

(3lg 2 – lg 24):(lg 3 + lg 27).

Answer 1

$dfrac{3 text{lg} 2 - text{lg} 24}{text{lg} 3 + text{lg} 27} = dfrac{text{lg} 2^{3} - text{lg} 24}{text{lg} 3 + text{lg} 27} = dfrac{text{lg} 8 - text{lg} 24}{text{lg} 3 + text{lg} 27} = dfrac{text{lg} dfrac{8}{24}}{text{lg} 3 cdotp 27} = dfrac{text{lg} dfrac{1}{3}}{text{lg} 81} =\\ = dfrac{text{lg} 3^{-1}}{text{lg} 3^{4}} = dfrac{-text{lg} 3}{4 text{lg} 3} = -dfrac{1}{4}$