Question

If 2x =5y =10z prove that 1÷x+1÷y=1÷z

Answer 1

Step-by-step explanation:

Let,  $2^{x}$=$5^{y}$= $10^{z}$= k

Therefore, $2^{x}$= k, 2 = $k^{1/x}$

                  $5^{y}$ = k, 5 =$k^{1/y}$

                  $10^{z}$ = k, 10 = $k^{1/z}$

Therefore,

               5*2 = 10

            or, $k^{1/y}$ * $k^{1/x}$ = $k^{1/z}$

           or, $k^{1/x + 1/y}$ =  $k^{1/z}$

           or, 1/x + 1/y = 1/z (proved)   [If bases are equal then powers are also  equal]

Answer 2

Answer:

Step-by-step explanation:

Let,  == = k

Therefore, = k, 2 =  

                  = k, 5 =

                  = k, 10 =  

Therefore,

              5*2 = 10

           or,  *  =  

          or,  =  

          or, 1/x + 1/y = 1/z (proved)   [If bases are equal then powers are also  equal]