Question

If 2^x=6^y=(18)^2, then prove that 2/y=1/x+1/z​

Answer 1

Step-by-step explanation:

2^x=6^y=(18)^z= k (say)

2^x=k

2=k^1/x............eq1

6^y=k

6=k^1/y

squiring both sides

36=k^2/y.......eq2

18^z=k

18=k^1/z....eq3

multiplying eq1 and eq3

2×18=k^1/x . k^1/z

36=k^(1/x+1/z)

k^2/y=k^(1/x+1/z) (putting the value from eq2)

2/y= 1/x+1/z proved. ( we know that if a^m=a^n then m=n)

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