Question

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

Answer 1

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