Question

help me in this Q. give me full solution plz

Answer 1

Hello Vanshika :  - ) 

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according to your question 
 
2 ^x  =  3^y  = 6^z is given right !  

so we can say that 

2 ^x  =  3^y  = 6^z = ( any constant k )

now we will take log to reduce this equation vanshika ^_^ ! 

log 2^x = log 3^y = log 6 ^z = log k 

now we use the property of logarithm as log a^n is written as n log a 

x log 2 = y log 3 = z log 6  = log k 

x log 2 = log k    1/x  =  log 2 / log k 

y log 3 = log k     1/y  =  log 3 / log k 

z log 6 = log k    1/z = log 6 / log k     so  1/z  = >  log ( 2 * 3)/ log k 

and using property of logarithm log ( a * b ) is written as log a + log b  

1/z = > log 2/log k + log 3 /log k 

hence prove  1/x + 1/y = 1/z because according to situation 

1/x = log 2 / log k and 1/y = log 3 / log k and 1/x + 1/ y = > log 2/log k   + log3 /log k  

so it means 1/x  + 1/ y = 1/z hence prove 

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HOPE THIS HELPS YOU 

@ ENGINEER GOPAL B-Tech IIT ROORKEY