簡約 log_{10}((6x^2-24x)/(6x(x+1)(x+3)))

解

簡約

lo g_{10} (\frac{6 x ^{2} - 24 x}{6 x ( x + 1 ) ( x + 3 )})

lo g_{10} (x - 4) - lo g_{10} (x + 1) - lo g_{10} (x + 3)

解答ステップ

lo g_{10} (\frac{6 x ^{2} - 24 x}{6 x ( x + 1 ) ( x + 3 )})

簡素化

\frac{6 x ^{2} - 24 x}{6 x ( x + 1 ) ( x + 3 )} : \frac{x - 4}{( x + 1 ) ( x + 3 )}

= lo g_{10} (\frac{x - 4}{( x + 1 ) ( x + 3 )})

対数の規則を適用する:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{x - 4}{( x + 1 ) ( x + 3 )}) = lo g_{10} (x - 4) - lo g_{10} ((x + 1) (x + 3))

= lo g_{10} (x - 4) - lo g_{10} ((x + 1) (x + 3))

簡素化

lo g_{10} ((x + 1) (x + 3)) : lo g_{10} (x + 1) + lo g_{10} (x + 3)

= lo g_{10} (x - 4) - (lo g_{10} (x + 1) + lo g_{10} (x + 3))

分配法則を適用する:

- (a + b) = - a - b

- (lo g_{10} (x + 1) + lo g_{10} (x + 3)) = - lo g_{10} (x + 1) - lo g_{10} (x + 3)

= lo g_{10} (x - 4) - lo g_{10} (x + 1) - lo g_{10} (x + 3)