Question

If 2^x = 3^y = 12^z , write an expression between x , y , z​

Answer 1

Answer:

The answer will be xy=z(x+2y)

Answer 2

Step-by-step explanation:

$\mathbb\red{ \tiny A \scriptsize \: N \small \:S \large \: W \Large \:E \huge \: R}$

$\begin{aligned} \rm 2^{x} &=3^{y}=12^{z}=k \text { (say) } & \\ \\ \Rightarrow & & \rm 2^{\frac{1}{2}} & \rm=k^{\frac{1}{x}}, 3=k^{\frac{1}{y}}, 12=k^{\frac{1}{z}} \\ \\ \Rightarrow & & \rm 12 & \rm=2 \times 2 \times 3 \\ \\ \Rightarrow & & \rm k^{\frac{1}{z}} & \rm=k^{\frac{1}{x}} \times k^{\frac{1}{x}} \times k^{\frac{1}{y}} \\ \\ \Rightarrow & & \rm k^{\frac{1}{z}} & \rm=k^{\frac{2}{x}+\frac{1}{y}} \\ \\ \Rightarrow & & \rm\frac{1}{z} & \rm=\frac{2}{x}+\frac{1}{y} \Rightarrow \frac{1}{z}=\frac{2 y+x}{x y} \\ \\ \Rightarrow & & \rm x y & \rm=z(x+2 y) \end{aligned}$