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We have to solve 13^x - 20 = 13^ (3 - x)

13^x - 20 = 13^ (3 - x)

=> 13^x - 20 = 13^3/ 13^x

let 13^x = y

=> y - 20 = 13^3 / y

=> y^2 - 20 y - 13^3 = 0

y1 = [20 + sqrt (20^2 + 4*13^3)]/ 2

= 10 + sqrt 2297

y2 = 10 - sqrt 2297

As 13^x = y

13^x = 10 + sqrt 2297

x log 13 = log (10 + sqrt 2297)

x = log (10 + sqrt 2297) / log 13

=> x = 1.5825 (approx)

Therefore x = log (10 + sqrt 2297) / log 13

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