2-a-3-b-36-c-then-prove-that-ab-2c-a-b-

Question Number 191839 by MATHEMATICSAM last updated on 01/May/23

2^{a} = 3^{b} = 36^{c} then prove that

a b = 2 c (a + b) .

Answered by AST last updated on 01/May/23

a = {b l o g}_{2} (3) \Rightarrow \frac{a}{b} = {l o g}_{2} (3) \Rightarrow \frac{a + b}{b} = {l o g}_{2} (6)

a = {c l o g}_{2} (36) \Rightarrow \frac{a}{c} = {l o g}_{2} (36) \Rightarrow \frac{a}{2 c} = {l o g}_{2} (6)

\Rightarrow \frac{a}{2 c} = \frac{a + b}{b} \Rightarrow a b = 2 c (a + b)

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