Para o bater com o gabarito, o enunciado correto é [tex3]x^n-1[/tex3]
na base [tex3]x[/tex3]
.
Aqui concluímos que [tex3]{x^n}_{10}={10^n}_x[/tex3]
.
Logo,
[tex3]{x^n}_{10}-1={10^n}_x-1[/tex3]
[tex3]{10^1}_{10}-1=10_{10}-1=9[/tex3]
[tex3]{10^2}_{10}-1=100_{10}-1=99[/tex3]
[tex3]{10^3}_{10}-1=1000_{10}-1=999[/tex3]
[tex3]{10^4}_{10}-1=10000_{10}-1=9999[/tex3]
[tex3]{2^1}_{2}-1=10_{2}-1=1[/tex3]
[tex3]{2^2}_{2}-1=100_{2}-1=11[/tex3]
[tex3]{2^3}_{2}-1=1000_{2}-1=111[/tex3]
[tex3]{2^4}_{2}-1=10000_{2}-1=1111[/tex3]
[tex3]{8^1}_{2}-1=10_{8}-1=7[/tex3]
[tex3]{8^2}_{2}-1=100_{8}-1=77[/tex3]
[tex3]{8^3}_{2}-1=1000_{8}-1=777[/tex3]
[tex3]{8^4}_{2}-1=10000_{8}-1=7777[/tex3]