I know if I have log(x)^7 it would be 7logx. But what if I had (log(x))^3. What would I do?

Answer 1

log(x^7) = 7logx = logx + logx + logx + logx + logx + logx + logx

(logx)^7 = logx(logx)(logx)(logx)(logx)(logx)(logx)

log(x^7) = sum of seven logx's

(logx)^7 = product of seven logx's

same two situations with log(x^3) and (logx)^3

1st = 3logx

but

2nd = logxlogxlogx

Answer 2

log(x³) = 3logx = logx + logx + logx, but (logx)³ = (logx)(logx)(logx)