the values of x and z that maximise ln(4-x) + ln(4+z) + ln(z), also

maximise:

(16-x^2)z ...(1)

as x>0, the constraint may be rewritten:

x^2(4-z)^=(32/7)^2,

or:

x=32/(7(4-z)) ...(2)

So substitute (2) into (1) and find the z that maximises this now

unconstrained objective, find the corresponding x from 2, and substitute

back into ln(4-x) + ln(4+z) + ln(z) to find its maximum.

RonL