Given that x, y, z are positive real numbers, and x-th power of 3=4 y-th power of y =6 z-th power of verification: z-th division 1 minus x-th division 1=2 y-th division 1

Given that x, y, z are positive real numbers, and x-th power of 3=4 y-th power of y =6 z-th power of verification: z-th division 1 minus x-th division 1=2 y-th division 1

Take log command simultaneously: xlg3=ylg4=zlg6=m
Then 1/x = lg3/m
1/Y = lg4/m
1/Z=lg6/m
1/Z -1/x =(lg 6- lg 3)/m = lg 2/m
1/(2Y)=(1/2) lg4/m = lg2/m
Get proof

Given positive real number xyz satisfies x power of 3= y power of 4= z power of 6, prove 1/z-1/x=1/zy

3^X=4^y=6^z
Ln (3^x)= ln (4^y)= ln (6^z)
Xln3=yln4=zln6
Xln3=2yln2= z (ln2+ln3)
Let xln3=2yln2=z (ln2+ln3)=t
Ln3=t/x, ln2=t/(2y), ln2+ln3=t/z
T/(2y)+t/x=t/z
1/(2Y)+1/x=1/z
1/Z-1/x =1/(2y)
Your topic is wrong.