4(2/3)^{x^2-5x+4}=9

解

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

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

十進法表記

x = 2, x = 3

解答ステップ

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

以下で両辺を割る

4

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

指数の規則を適用する

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

解く

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

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