Germany| A Nice Math Olympiad exponential problem |Can you solve this?

This is a math Olympiad exponential question. The solution was obtained using the laws of indices or exponentials and also the laws of the logarithm. #matholympiadproblem #exponentialequations #logarithm #olympiadmathematics

[@RyanLewis-Johnson-wq6xs]

1/Log[2,216]+1/Log[3,216]=0.3 recurring

[@RyanLewis-Johnson-wq6xs]

1/(Log[3,216]+Log[2,216])=(Log10[2^Log10[3]])/(Log10[216^Log10[6]]) 2^(Log[2,1.6875]+7)=216 3^(Log[3,2+0.6/0.9]+4)=216 x= Log[2,1.6875]+7 y=Log[3,2+0.6/0.9]+4

[@SViyaasJayavel]

Short form 2^x=216 2=216^(1/x) 3=216^(1/y) Multiple 2 equations 6=216^(1/x+1/y) 216^1/3=216^(1/x+1/y) Therefore 1/x+1/y=1/3

[@RyanLewis-Johnson-wq6xs]

1/(Log[3,216]+Log[2,216])=Log[216^Log10[6],2^Log10[3]]

[@prime423]

You are a good teacher!!Patient and detailed. Two suggestions. First ,if X is a variable use a dot for multiplication.Secondly,one could take the log to any base. What about base 2?

[@JJONLINEMATHSCLASSchannel]

Thanks so much for your contribution

[@shahidrasul9580]

Mam, with respect, I have many times request you, plz explain Extraneous roots...?❤

[@JJONLINEMATHSCLASSchannel]

Okay sure

[@shahidrasul9580]

Thanks, i am Shahid Rasul from Pakistan, city JHELUM ​@@JJONLINEMATHSCLASSchannel

[@winstonbartley9851]

You need to do more explanation

[@winstonbartley9851]

How did you get 6

[@EkomobongEtuk]

👏

[@JJONLINEMATHSCLASSchannel]

Thanks

[@jaybazu]

Where did you get the 6 from please?

[@JJONLINEMATHSCLASSchannel]

6 raised to the power of 3 is 216. So it is another way you can write 216

[@jaybazu]

@@JJONLINEMATHSCLASSchannel Yes I checked that... In your solution it went too fast... But great I left those things more than 30 years ago

[@RyanLewis-Johnson-wq6xs]

I didn’t use a calculator

[@JJONLINEMATHSCLASSchannel]

👏👏👏👏

[@Extratremendouszeus]

Welcome darling😅

[@JJONLINEMATHSCLASSchannel]

❤️❤️

[@fernandoarielgarcia5498]

You are a Genius women and very beautiful😊😍😍😘😘. What's country?

[@fernandoarielgarcia5498]

What's your country dear?

[@wayneyadams]

Is she speaking English?