log[base x1] log[base x2]...log[base xn](xn^xn-1^xn-2^...x1)

Question

log_x1 log_x2...... log_xn-1log_xn (xn^{xn-1^xn-2^....x1})

Answer 1

log_xn(((xn^xn-1)^xn-2)^xn-3)...)^x1 = ((((x_{n - 1})^xn-2)^xn-3)^xn-4) ...)^x1

log_xn-1(all of the above left) = (((x_{n - 1})(x_{n - 2})^xn-3)^xn-4) ...)^x1

 

This leads to:

 

(x_{n - 1})(x_{n - 2})(x_{n - 3})...(x₁)