A Non standard Logarithmic Equation with Different Bases

[@interstigation]

If you are using derivative anyway, why don't you just differentiate the original function? That is, differentiate log_3(x+1) - log_4(x+8) to get 1/(x+1)(ln 3) - 1/(x+8)(ln 4) which is quite obviously positive for all x > -1 (the domain of the original function), so there can be at most one real solution. Great video btw! Props from a fellow KZbinr here.

[@gyankahub1]

Very good way to explain

[@gyankahub1]

Very nice and knowledgeable video

[@maxvangulik1988]

ln(a+1)/ln(3)=ln(a+8)/ln(4) ln(a+1)/ln(a+8)=ln(3)/ln(4) ln(a+1)/ln(a+8)=ln(9)/ln(16) because squaring the input will just bring a factor of 1/2 outside and it cancels in the top and bottom a=8

[@noeticresearch]

I missed your trademark "smiley face" at the end of the video. :-) Great video on different logarithmic bases!

[@ShortsOfSyber]

Sorry! 😔

[@paulor.r.correia1789]

Excelente. Excelent 🇧🇷🇧🇷🇧🇷

[@에스피-h8t]

Solution by insight log _3 (9)=log _4(16)=2 a=8

[@p12psicop]

Your minimum point for your graph is a smiley face.

[@ShortsOfSyber]

🙃

[@karajkot6735]

I think instead analyzing 4^x-3^x=7, you should have analyzed 4^x and 3^x+ 7, and analyse intersection. That would be easier.

[@ShortsOfSyber]

Good thinking

[@karajkot6735]

@@ShortsOfSyber I mean you don't need any derivative and all to analyze in this case.

[@MaheshKumar-lx1ku]

@@ShortsOfSyber you makes a simple prblm difficult 🤬

[@user-lu6yg3vk9z]

Keep up the great content.

[@ShortsOfSyber]

Thanks, will do!

[@user-lu6yg3vk9z]

@@ShortsOfSyber is there anyway you can do some calculus integration techniques would be nice.

[@ilyashick3178]

Answer a=3^log_4_ (7) -1

[@atanuroy3548]

X will be 2 and a will be 8 simply without too long process.

[@kianmath71]

a = 8