Question

If 2^x=3^y=12^z, prove that x=2yz/y-z​
A) x
B) 2y
C) −z
D) 2x
​

Answer 1

To prove that x=2yz/(y-z), we start by expressing each term in terms of a common base. We then set two of the terms equal to each other and solve for x. Substituting the value of x into the expression x=2yz/(y-z), we find that x=2yz/(y-z) holds true.

Step-by-step explanation:

To prove that x=2yz/(y-z) when 2^x=3^y=12^z, we will first express each term in terms of a common base:

2^x = (2^x)/(2^0) = (2^x)/(3^0) = (2^x)/(12^0)

3^y = (3^0)/(3^0) = (2^0)/(3^0) = (2^0)/(12^0)

12^z = (2^0)/(2^0) = (3^0)/(2^0) = (2^0)/(12^0)

Since all the terms are equal to each other, we can set any two terms equal to each other and solve for x:

(2^x)/(2^0) = (2^0)/(12^0)

2^x = (2^0)/(12^0)

x = 0

Substituting this value of x into the expression x=2yz/(y-z), we get:

x = 2yz/(y-z)

0 = 2yz/(y-z)

0 = 2yz

Since 0 = 2yz, we can conclude that x = 2yz/(y-z).