Question

if 2^x=3^y=12^z , show that 1/z =1/y + 1/x .​

Answer 1

Answer:

Let 2

x

=3

y

=12

z

=k.

Then, 2=k

1/x

,3=k

1/y

and 12=k

1/z

Now, 12=k

1/z

⇒2

2

×3=k

1/z

⇒(k

1/x

)

2

×k

1/y

=k

1/z

[∵2=k

1/x

and 3=k

1/y

]

⇒

k

x

2

+

k

z

1

⇒

x

2

+

y

1

=

z

1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Let 2

x

=3

y

=12

z

=k.

Then, 2=k

1/x

,3=k

1/y

and 12=k

1/z

Now, 12=k

1/z

⇒2

2

×3=k

1/z

⇒(k

1/x

)

2

×k

1/y

=k

1/z

[∵2=k

1/x

and 3=k

1/y

]

⇒

k

x

2

+

k

z

1

⇒

x

2

+

y

1

=

z

1