Question

If 2^a = 3^b = 6^c then show that c = ab divide
a+b​

Answer 1

$let \: {2}^{a} = k \\ 2 = {k}^{ \frac{1}{a} } \\ similarly \\ 3 = {k}^{ \frac{1}{b} } \\ 6 = {k}^{ \frac{1}{c} } \\ as \: 6 = {k}^{ \frac{1}{c} } \\ 2 \times 3 = {k}^{ \frac{1}{c} } { \frac{}{} }^{} \\ {k}^{ \frac{1}{a} } \times {k}^{ \frac{1}{b} } = {k}^{ \frac{1}{c} } \\ \frac{1}{a} \times \frac{1}{b} = \frac{1}{c} \\ ab = c$
hope this helps you