Takamori37
Untuk 0,9090... Anggaplah: 0,9090... = a Sehingga: 90,9090... = 100a
Kurangi keduanya: 100a = 90,9090... ~~~a = 0,9090... - 99a = 90 a = 90/99 a = 10/11
Sehingga (asumsi a adalah basis): a log 1331 = a log 11³ = 3 x a log 11 = 3 x 1 / ¹¹log a = 3 x 1/ ¹¹log(10/11) = 3 x 1/[¹¹log 10 - ¹¹log 11] = 3 / [¹¹log 10 - 1]
Anggaplah:
0,9090... = a
Sehingga:
90,9090... = 100a
Kurangi keduanya:
100a = 90,9090...
~~~a = 0,9090... -
99a = 90
a = 90/99
a = 10/11
Sehingga (asumsi a adalah basis):
a log 1331
= a log 11³
= 3 x a log 11
= 3 x 1 / ¹¹log a
= 3 x 1/ ¹¹log(10/11)
= 3 x 1/[¹¹log 10 - ¹¹log 11]
= 3 / [¹¹log 10 - 1]
Atau:
= 3 / [1/log 11 - 1]
= 3 / [1/log 11 (1 - log 11)]
= [3 x log 11] / [1 - log 11]