maths---sequences

log10k ,log10k^2, log10k^3 , log10k^4
log10k^2-log10k=2log10k-log10k=log10k
log10k^3-log10k^2=3log10k-2log10k=log10k
log10k^(n+1)-log10k^n=(n+1)log10k-nlog10k=log10k
so log10k ,log10k^2, log10k^3 , log10k^4.....where k > 0 is an arithmetic sequence
first term is log10k , common difference is log10k
general term
= log10k +(n-1) log10k
=n log10k
= log10k ^n
for log(10k)^2 ,log(10k^2)^2, log(10k^2)^3 , log(10k^2)^4.....
log(10k^2)^2-log(10k^2)=2log(10k^2)-log(10k^2)=log(10k^2)
log(10k^2)^3-log(10k^2)^2=3log(10k^2)-2log(10k^2)=log(10k^2)
log(10k^2)^(n+1)-log(10k^2)^n=(n+1)log(10k^2)-nlog(10k^2)=log(10k^2)
so log(10k)^2 ,log(10k^2)^2, log(10k^2)^3 , log(10k^2)^4.....where k > 0 is an arithmetic sequence
first term=log(10k^2) , common difference=log(10k^2)
general term
=log(10k^2) +(n-1)log(10k^2)
=nlog(10k^2)
=log(10k^2) ^n