15^{4a}=81^{a+2}

解

1 5^{4 a} = 8 1^{a + 2}

a = \frac{2 ln ( 3 )}{ln ( 5 )}

十進法表記

a = 1.36521 \dots

解答ステップ

1 5^{4 a} = 8 1^{a + 2}

指数の規則を適用する

4 a ln (15) = (a + 2) ln (81)

解く

4 a ln (15) = (a + 2) ln (81) : a = \frac{2 ln ( 3 )}{ln ( 5 )}

a = \frac{2 ln ( 3 )}{ln ( 5 )}