3-a-7-b-441-ab-a-b-

Question Number 195428 by mathlove last updated on 02/Aug/23

3^{a} = 7^{b} = 441

\frac{a b}{a + b} = ?

Answered by Frix last updated on 02/Aug/23

441 = 3^{2} 7^{2}

a = 2 (1 + \frac{\ln 7}{\ln 3}) = 2 (1 + r)

b = 2 (1 + \frac{\ln 3}{\ln 7}) = 2 (1 + r^{- 1})

\frac{a b}{a + b} = \frac{\frac{4 {(r + 1)}^{2}}{r}}{\frac{2 {(r + 1)}^{2}}{r}} = 2

Answered by sandy_delta last updated on 02/Aug/23

3^{a} \times 7^{b} = 441^{2}

3^{a} \times 7^{b} = {(3^{2} . 7^{2})}^{2}

3^{a} \times 7^{b} = 3^{4} . 7^{4}

so a = 4 and b = 4

\frac{ab}{a + b} = \frac{4.4}{4 + 4} = 2