SOLUTION: Given 2^x=3^y=5^z=900^w Show that: xyz=2w(xy+yz+xz)

Suppose that 

2x = 3y = 5z = 900w = A

Then,

ln(2x) = ln(3y) = ln(5z) = ln(900w) = ln(A)

x·ln(2) = y·ln(3) = z·ln(5) = w·ln(900) = ln(A)

, , , 

*** xyz =  = ***       

xy =  = 

yz =  = 

xz =  =   

xy + yz + xz = 

          



          

So 2w =    
    
2w(xy+yz+xz)

          

And that's what xyz was shown equal to above, marked ***      

Edwin

Suppose that

2x = 3y = 5z = 900w = A

Then (you can also use log instead of ln, as above):

log(2x) = log(3y) = log(5z) = log(900w) = log(A)

x·log(2) = y·log(3) = z·log(5) = w·log(900) = log(A)

, , , 

*** xyz =  = ***

xy =  = 

yz =  = 

xz =  = 

xy + yz + xz = 

          



          

So 2w = 

2w(xy+yz+xz)

          

And that's what xyz was shown equal to above, marked ***

Edwin