Jawaban:

Untuk menyelesaikan masalah ini, kita dapat menggunakan sifat logaritma untuk menuliskan persamaan-persamaan yang diberikan dalam bentuk yang lebih mudah diolah.

2^x - 2^y = 1

2^x - 2^y = 12^y = 2^x - 1

2^x - 2^y = 12^y = 2^x - 1y = x - 1

2^x - 2^y = 12^y = 2^x - 1y = x - 14^x - 4^y = 5/3

2^x - 2^y = 12^y = 2^x - 1y = x - 14^x - 4^y = 5/34^y = 4^x - 5/3

2^x - 2^y = 12^y = 2^x - 1y = x - 14^x - 4^y = 5/34^y = 4^x - 5/3y = (x - log4(5/3))/log4(4)

Setelah itu, kita dapat menyelesaikan sistem persamaan tersebut dengan menyamakan x - 1 dengan (x - log4(5/3))/log4(4).

x - 1 = (x - log4(5/3))/log4(4)

x - 1 = (x - log4(5/3))/log4(4)x - log4(4) = (x - log4(5/3))/log4(4)

x - 1 = (x - log4(5/3))/log4(4)x - log4(4) = (x - log4(5/3))/log4(4)x = (x - log4(5/3))/log4(4) + log4(4)

Kita dapat menyederhanakan persamaan tersebut dengan menggunakan sifat logaritma.

x = (x - log4(5/3) + log4(5/3))/log4(4) + log4(4)

x = (x - log4(5/3) + log4(5/3))/log4(4) + log4(4)x = (x + log4(5/3))/log4(4) + log4(4)

Setelah itu, kita dapat menyelesaikan persamaan tersebut dengan menggunakan sifat logaritma lainnya.

x = (x + log4(5/3))/log4(4) + log4(4)

x = (x + log4(5/3))/log4(4) + log4(4)x = x/log4(4) + log4(4) + log4(5/3)/log4(4)

x = (x + log4(5/3))/log4(4) + log4(4)x = x/log4(4) + log4(4) + log4(5/3)/log4(4)x = x/log4(4) + log4(4) + log4(5) - log4(3)/log4(4)

x = (x + log4(5/3))/log4(4) + log4(4)x = x/log4(4) + log4(4) + log4(5/3)/log4(4)x = x/log4(4) + log4(4) + log4(5) - log4(3)/log4(4)x = x/log4(4) + log4(5) - log4(3) + log4(4)

x = (x + log4(5/3))/log4(4) + log4(4)x = x/log4(4) + log4(4) + log4(5/3)/log4(4)x = x/log4(4) + log4(4) + log4(5) - log4(3)/log4(4)x = x/log4(4) + log4(5) - log4(3) + log4(4)x = x/log4(4) + log4(5) - log4(3) + 1

x = (x + log4(5/3))/log4(4) + log4(4)x = x/log4(4) + log4(4) + log4(5/3)/log4(4)x = x/log4(4) + log4(4) + log4(5) - log4(3)/log4(4)x = x/log4(4) + log4(5) - log4(3) + log4(4)x = x/log4(4) + log4(5) - log4(3) + 1x = x/log4(4) + log4(5) - log4(3) + 1

x = (x + log4(5/3))/log4(4) + log4(4)x = x/log4(4) + log4(4) + log4(5/3)/log4(4)x = x/log4(4) + log4(4) + log4(5) - log4(3)/log4(4)x = x/log4(4) + log4(5) - log4(3) + log4(4)x = x/log4(4) + log4(5) - log4(3) + 1x = x/log4(4) + log4(5) - log4(3) + 1x = x/1 + log4(5) - log4(3) + 1

x = (x + log4(5/3))/log4(4) + log4(4)x = x/log4(4) + log4(4) + log4(5/3)/log4(4)x = x/log4(4) + log4(4) + log4(5) - log4(3)/log4(4)x = x/log4(4) + log4(5) - log4(3) + log4(4)x = x/log4(4) + log4(5) - log4(3) + 1x = x/log4(4) + log4(5) - log4(3) + 1x = x/1 + log4(5) - log4(3) + 1x = x + log4(5) - log4(3) + 1

Kita dapat menyederhanakan persamaan tersebut dengan menggunakan sifat logaritma lainnya.

x = x + log4(5) - log4(3) + 1

x = x + log4(5) - log4(3) + 1x = x + log4(5/3) + 1

x = x + log4(5) - log4(3) + 1x = x + log4(5/3) + 1x = x + log4(5/3) + log4(4/4)

x = x + log4(5) - log4(3) + 1x = x + log4(5/3) + 1x = x + log4(5/3) + log4(4/4)x = x + log4(5/34/4)

x = x + log4(5) - log4(3) + 1x = x + log4(5/3) + 1x = x + log4(5/3) + log4(4/4)x = x + log4(5/34/4)x = x + log4(5/32^2/2^2)

x = x + log4(5) - log4(3) + 1x = x + log4(5/3) + 1x = x + log4(5/3) + log4(4/4)x = x + log4(5/34/4)x = x + log4(5/32^2/2^2)x = x + log4(5/32^2/2^2)

x = x + log4(5) - log4(3) + 1x = x + log4(5/3) + 1x = x + log4(5/3) + log4(4/4)x = x + log4(5/34/4)x = x + log4(5/32^2/2^2)x = x + log4(5/32^2/2^2)x = x + log4(5/32^2/2^2)