Question

If 2^x = 3y = 12^z prove that x =
2yz/y-z​

Answer 1

Answer:

Now, the logarithmic solution has been thoroughly explained. I'll show a way to do this without them.

Given: 2x=3y=12z

Required to prove:

x=2yzy−z

Simplifying,

1x=y−z2yz

1x=y2yz−z2yz

1x=12z−12y

1x=1/2⋅(1z−1y)

We can divide by x,y and z because they are not zero. While this does satisfy the given but the value of the statement we are required to prove becomes undefined.

Now, let

2x=3y=12z=k

Then,

2x=k→2=k1x

3y=k→3=k1y

12z=k→12=k1z

So,

12=k1z

12/3=k1zk1y

4=k1zk1y

4=k1z−1y

41/2=(k1z−1y)12

2=(k12z−12y)

k1x=(k12z−12y)

Comparing exponents,

1x=(12z−12y)

[Remember this?]

1x=y−z2yz

x=2yzy−z