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vanshiangel
@vanshiangel
July 2021
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help me in this Q. give me full solution plz
Answers & Comments
enrique
Hello Vanshika : - )
==========================================================
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
=================================================================
HOPE THIS HELPS YOU
@ ENGINEER GOPAL B-Tech IIT ROORKEY
4 votes
Thanks 4
Priyanshu360
wow critical ans bro..
enrique
Np bro bro :-)
enrique
Thnx
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Answers & Comments
==========================================================
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
=================================================================
HOPE THIS HELPS YOU
@ ENGINEER GOPAL B-Tech IIT ROORKEY