展開する ln((2x+1)^{1/(ln(x))})

解

展開する

ln ((2 x + 1)^{\frac{1}{l n ( x )}})

\frac{ln ( 2 x + 1 )}{ln ( x )}

解答ステップ

ln ((2 x + 1)^{\frac{1}{l n ( x )}})

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((2 x + 1)^{\frac{1}{l n ( x )}}) = \frac{1}{ln ( x )} ln (2 x + 1)

= \frac{1}{ln ( x )} ln (2 x + 1)

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot ln ( 2 x + 1 )}{ln ( x )}

乗算:

1 \cdot ln (2 x + 1) = ln (2 x + 1)

= \frac{ln ( 2 x + 1 )}{ln ( x )}