Question

If $2^a=3^b=6^c$ then show that $c=\frac{ab}{a+b}$

Answer 1

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

$alog2=blog3=clog6=K$(say)

$\therefore C=\frac{K}{log6}$

and $log2=\frac{K}{a}$ and $log3=\frac{K}{b}$

$\therefore C=\frac{K}{log2+log3}$

$=\frac{K}{K/a+K/b}$

$\therefore C=\frac{ab}{a+b}$