3/4[3lnx+lny+2/3lnz-ln5-3lnw-2lnw]

Question

Condense the equation , exponential & longarithmic

Answer 1

The logs can be combined where adding becomes multiplication and subtraction division:

¾[ln(x³yz^⅔/(5w⁵)]=ln(x^9/4y^¾√z/(5^¾w^15/4).

3ln(w)+2ln(w)=5ln(w)=ln(w)+ln(w)+ln(w)+ln(w)+ln(w)=ln(w×w×w×w×w)=ln(w⁵), for example. This is how a multiple of a log is interpreted: the multiple is converted to an exponent, which can be any value, including a fraction. Note also that z^½ is the same as √z; 5^¾ is the same as ⁴√5³ or ⁴√125.