A Very Nice Math Olympiad Problem | Solve for x | Algebra

[@mikeeisler6463]

X = 7 not 12

[@MichaelIdoro]

21:19 Yeah, he made a mistake by writing 10 instead of 5

[@taniacsibi6879]

X=7 not 12

[@lornacy]

Yeah, it was a lovely solution but they stumbled on the landing 😂 Honestly if it was me I would have probably got the signs wrong somewhere so I don't judge.

[@RashmiRay-c1y]

The equation implies [log(5x-25)][log(x-5)] = log 2. Let x-5=t. Then, log t[log t + log 5] = log 2 = log (10/5) = 1 - log 5. Thus, (log t)^2 + (log 5)(log t) + log 5 -1 =0 > log t = -1, 1-log 5. If log t = -1 > t = 1/10 > x = 51/10. If log t = 1-log 5 = log 10 - log 5 = log (10/5) = log 2, t = 2 > x=7. So, x = 51/10, 7.

[@SpencersAcademy]

Excellent! 👏