Question

If $2^a=3^b=6^c$ then C cannot be equal to

• A. $\frac{a+b}{ab}$
• B. $\frac{ab}{a+b}$
• C. $\frac{a-b}{ab}$
• D. $\frac{ab}{a-b}$

Answer 1

Answer: (A), (C), (D)

The correct options are
A $\frac{a+b}{ab}$
C $\frac{a-b}{ab}$
D $\frac{ab}{a-b}$

$2^a=3^b=6^c$

As $2^a=6^c\Rightarrow 2=6^{\frac{c}{a}}$ ______ (1)

& $3^b=6^c\Rightarrow 3=6^{\frac{c}{b}}$ _____ (2)

Multiply (1) & (2)

$\Rightarrow 6=6^{\frac{c}{a}+\frac{c}{b}}\Rightarrow \frac{c}{a}+\frac{c}{b}=1$

$\Rightarrow c=\frac{ab}{a+b}$