Germany | Can you solve this? | Math Olympiad

[@samuelkelly2197]

You can never go wrong with Master T Maths Class. I think Master T needs to have a book titled Step by Step Solution to solving Problems in Logarithms and Indices. A have a similar book I hope to share with Master T when I get his contact details. Master T is a CLASS ACT. BRAVO Sir !!! You are so good and what I admire most about your lecture is most is when we are checking whether our answer in right. Any good tutorials. Times spent listening to You is time well spent Sir !!!

[@RyanLewis-Johnson-wq6xs]

8^(Log[8,1.230769 recurring ]+2)+8^Log[8,1.230769 recurring ]=80 Input interpretation 8^(log(8, 1.(230769)^_ (repeating decimal)) + 2) + 8^log(8, 1.(230769)^_ (repeating decimal)) = 80 x=(4-Log[2,13])/3=Log[8,16/13] Result True

[@ЛюдмилаИщенко]

Записан ответ и обведён в рамку.... А где же 2 из знаменателя под логарифмом?

[@andresrebolledobanquet1924]

8x + 16 + 8x = 80 16x = 80 - 16 16x = 64 x = log 64 /log 16 x = 1.5 16^1.5 = 64

[@MasterTMathsClass]

✌️

[@AlexanderSemashkevich]

8^x(8²+1)=80 8^x=16/13 x=(log16-log13)/log8=(4log2-log13)/3log2=4/3-log13/3log2 Find log13: log12=2log2+log3 log14=log2+log7 log13≈(log12+log14)/2≈(3log2+log3+log7)/2 So x≈4/3-(3log2+log3+log7)/6log2≈4/3-½-(log3+log7)/6log2≈⅚-(log3+log7)/6log2 x≈⅚-(0.477+0.845)/(6×0.301)≈⅚-661/903≈(5×903-6×661)/(6×903)≈183/1806≈0.1 8^(0.1+2)+8^0.1≈80.02