Find an expression in term of a and b, for c

Question

Given that 101^a =103^b = 10403^c

Answer 1

101^a + 103^b = 10403^c = (101(103))^c = 101^c(103)^c

c = a/(1+log103 to the base 101) + b/(1+ log101 to the base 103)

c = a(1+ln103/ln101) + b/(1+ ln101/ln103)

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