Math Olympiad Problem | Germany | How to solve!!!

[@doyouknoworjustbelieve6694]

8 = 2^3 So the equation becomes 2^(6a) = 200 6a. Log2 (2) = log2(2 x 2 x 2 x25) 6a = 3+ log2(25) 6a = 3+ 2 x log2(5) a = (1/2) + (1/3)log2(5)

[@sas9170]

1

[@MrLinusK]

Found a lot simpler solution... 8^a*8^a = 200 log2(8^a*8^a) = log2(200) log2(8^a) + log2(8^a) = log2(200) 2*a*log2(8) = log2(200) 6a=log2(200) a=log2(200)/6

[@quokka_yt]

I did it like so: 8ᵃ ⋅ 8ᵃ= 200 (8ᵃ)² = 200 8²ᵃ = 200 log₈ (8²ᵃ) = log₈ 200 2a = log₈ (8 ⋅ 25) 2a = log₈ 8 + log₈ 25 2a = 1 + log₈ 25 a = (1 + log₈ 25) / 2 ≈ 1,274

[@wolemai]

Big problem here! At time 7.20 you said that a log b = log a ^b and you based the following calculations on this. This is NOT correct! a log b = log b^a .