5002^d=503^d

解

500 \cdot 2^{d} = 50 \cdot 3^{d}

d = \frac{ln ( 10 )}{ln ( 3 ) - ln ( 2 )}

十進法表記

d = 5.67887 \dots

解答ステップ

500 \cdot 2^{d} = 50 \cdot 3^{d}

指数の規則を適用する

ln (500) + d ln (2) = ln (50) + d ln (3)

解く

ln (500) + d ln (2) = ln (50) + d ln (3) : d = \frac{ln ( 10 )}{ln ( 3 ) - ln ( 2 )}

d = \frac{ln ( 10 )}{ln ( 3 ) - ln ( 2 )}