How do i express this to exponential form?

a) log√2(w^2 x^3/y^5 z^7)

b) log(x^2 y^3 √z-1)

Beats me. A log is a log, not an exponential form.

You have 1/2 log2 + 2logw + 3logx - 5logy - 7logz

similarly for (b)

do you have an example of another problem which is solved, indicating what you wish to achieve?