3^{27^{x-2}}=9^{9^{x+1}}

解

3^{2 7^{x - 2}} = 9^{9^{x + 1}}

x = \frac{ln ( 2 ) + 8 ln ( 3 )}{ln ( 3 )}

十進法表記

x = 8.63092 \dots

解答ステップ

3^{2 7^{x - 2}} = 9^{9^{x + 1}}

指数の規則を適用する

3 (x - 2) ln (3) = ln (2) + 2 (x + 1) ln (3)

解く

3 (x - 2) ln (3) = ln (2) + 2 (x + 1) ln (3) : x = \frac{ln ( 2 ) + 8 ln ( 3 )}{ln ( 3 )}

x = \frac{ln ( 2 ) + 8 ln ( 3 )}{ln ( 3 )}