Question

If 2x = 3y = 12z, then show that 1/z = 1/y + 2/x​

Answer 1

Answer:

Step-by-step explanation:

Solution:

Given  

2^{x}= 3^{y}= (12)^{z}

Let \: 2^{x}= 3^{y}= (12)^{z}=k

i) 2^{x}=k \implies 2=k^{\frac{1}{x}}--(1)

ii)3^{y}=k \implies 3=k^{\frac{1}{y}}---(2)

iii)(12)^{z}=k \implies 12=k^{\frac{1}{z}}--(3)

Now,

\implies12=k^{\frac{1}{z}}

\implies 2^{2}\times 3=k^{\frac{1}{z}}

\implies k^{\frac{2}{x}}\times k^{\frac{1}{y}}=k^{\frac{1}{z}}

\implies k^{\frac{2}{x}+\frac{1}{y}}=k^{\frac{1}{z}}

\boxed { a^{m} × a^{n} = a^{m+n}}

\implies\frac{2}{x}+\frac{1}{y}=\frac{1}{z}

\boxed {If \: a^{m} = a^{n} \implies m = n}  

Hence , proved

••••