Math, asked by ssanjithkumar2006, 9 months ago

find the relationship between a,b and c .if 5^a=3^b=225^c. where a≠b,b≠c and c≠a.

Answers

Answered by gjenagjena66

5

${5}^{a} = {3}^{b} = {225}^{c} = k \\ \\ {k}^{ \frac{1}{a} } = 5 \\ \\ {k}^{ \frac{1}{b} } = 3 \\ \\ {k}^{ \frac{1}{c} } = 225 \\ \\ {k}^{ \frac{1}{c} } = {15}^{2} \\ \\ = {(5 \times 3)}^{2} \\ \\ {k}^{ \frac{1}{c} } = { ({k}^{ \frac{1}{a} } \times {k}^{ \frac{1}{b} } ) }^{2} \\ \\ \frac{1}{c} = \frac{2}{a} + \frac{2}{b}$

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