Question

If 2^x = 3^y = 12^z then find the value of x in terms of y & z. Please write the answer step by step​

Answer 1

$\huge \mathfrak \blue{answer}$

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