25^x - 15^x = 9^x

 

25^x - 15^x = 9^x

25^x/9^x - 15^x/9^x = 9^x/9^x

(25/9)^x - (15/9)^x = 1

(5/3)^2x - (5/3)^x = 1

[(5/3)^x]^2 - (5/3)^x - 1 = 0

Façamos 

(5/3)^x = y; y>0

y²-y -1 = 0

y = [1+ sqrt (5)]/2

ln (5/3)^x = ln [1+ sqrt (5)]/2

x ln (5/3) = ln [1+ sqrt (5)]/2

x ln (5/3) = ln [1+ sqrt (5)] - ln 2

x = ln [1+ sqrt (5)] - ln 2 / [ln (5/3)]

x = ln [1+ sqrt (5)] - ln 2 / [ln 5 - ln 3]

Jamal Malik