Question

2^a=3^b=12^c then 1/c-1/b-2/a=

Answer 1

Hi ..dear....
here is your solution...

Answer 2

Answer:

The answer is 0.

Step-by-step explanation:

We have,

$2^a=3^b=12^c$

Let,

$2^a=3^b=12^c=k$

$2^a=k\implies (2^a)^2=k^2\implies 4^a=k^2\implies m^\frac{2}{a}= 4$ ----(1),

$3^b=k\implies k^\frac{1}{b}=3$ -----(2),

$12^c=k\implies k^\frac{1}{c}=12$ ------(3)

Now,

$k^{\frac{1}{c}-\frac{1}{b}-\frac{2}{a}}$

$=k^{\frac{1}{c}-(\frac{1}{b}+\frac{2}{a})}$

$=\frac{k^{\frac{1}{c}}}{k^{\frac{1}{b}+\frac{2}{a}}}$   $(a^{m-n}=\frac{a^m}{a^n})$

$=\frac{k^{\frac{1}{c}}}{k^\frac{1}{b}.k^\frac{2}{a}}$  $(a^m.a^n=a^{m+n})$

$=\frac{12}{3\times 4}$  ( From equation (1), (2) and (3) )

$=\frac{12}{12}$

$=1$

$=k^0$

$\implies \frac{1}{c}-\frac{1}{b}-\frac{2}{a}=0$

$(a^m=a^n\implies m=n)$