3*6^x=4.5(e^2)^x

解

3 \cdot 6^{x} = 4.5 (e^{2})^{x}

x = \frac{ln ( 4.5 ) - ln ( 3 )}{ln ( 6 ) - 2}

十進法表記

x = - 1.94709 \dots

解答ステップ

3 \cdot 6^{x} = 4.5 (e^{2})^{x}

指数の規則を適用する

ln (3) + x ln (6) = ln (4.5) + 2 x

解く

ln (3) + x ln (6) = ln (4.5) + 2 x : x = \frac{ln ( 4.5 ) - ln ( 3 )}{ln ( 6 ) - 2}

x = \frac{ln ( 4.5 ) - ln ( 3 )}{ln ( 6 ) - 2}