38.5^x=6.5^{(x-2)}

解

38. 5^{x} = 6. 5^{(x - 2)}

x = - \frac{2 ln ( 6.5 )}{ln ( 38.5 ) - ln ( 6.5 )}

十進法表記

x = - 2.10450 \dots

解答ステップ

38. 5^{x} = 6. 5^{(x - 2)}

指数の規則を適用する

x ln (38.5) = (x - 2) ln (6.5)

解く

x ln (38.5) = (x - 2) ln (6.5) : x = - \frac{2 ln ( 6.5 )}{ln ( 38.5 ) - ln ( 6.5 )}

x = - \frac{2 ln ( 6.5 )}{ln ( 38.5 ) - ln ( 6.5 )}