Can someone please help me with these optimisation questions finding it very difficult (ps have given what i think is valid answer to q1 but cant do q2 at all.)

note: 2^6 measn 2 to the power of 6,

note: theta is a capital theta

note: log c (a) means log to the base c of a

1) Let a, b, c be positive real numbers. Show that loga(b) = logc(b)/ logc(a).

( i think i have the answer to this can someone pls confirm this is a thoroguh enough proof

let y= log a (b)

then a^y =b

so taking logarithms to the base c gives

log c (a^y)= log c (b)

implying

ylog c(a) = log c (b)

so: y = log c (b)/log c (a)

giving answer

2) Let a, b be real numbers, with a>0 and b > 0. Show (n + a)^b = theta(n^b). Show that (log n)^b = o(n^a). (For concreteness let’s take ‘log’ to mean ‘log2’.

thanx edgar