簡約 9/10 ln(2x+4)-12/5 ln(x+3)

解

簡約

\frac{9}{10} ln (2 x + 4) - \frac{12}{5} ln (x + 3)

ln (\frac{( 2 x + 4 ) ^{\frac{9}{10}}}{( x + 3 ) ^{\frac{12}{5}}})

解答ステップ

\frac{9}{10} ln (2 x + 4) - \frac{12}{5} ln (x + 3)

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{9}{10} ln (2 x + 4) = ln ((2 x + 4)^{\frac{9}{10}})

= ln ((2 x + 4)^{\frac{9}{10}}) - \frac{12}{5} ln (x + 3)

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{12}{5} ln (x + 3) = ln ((x + 3)^{\frac{12}{5}})

= ln ((2 x + 4)^{\frac{9}{10}}) - ln ((x + 3)^{\frac{12}{5}})

対数の規則を適用する:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln ((2 x + 4)^{\frac{9}{10}}) - ln ((x + 3)^{\frac{12}{5}}) = ln (\frac{( 2 x + 4 ) ^{\frac{9}{10}}}{( x + 3 ) ^{\frac{12}{5}}})

= ln (\frac{( 2 x + 4 ) ^{\frac{9}{10}}}{( x + 3 ) ^{\frac{12}{5}}})