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 UA-camr here.
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
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 UA-camr here.
Very good way to explain
Very nice and knowledgeable video
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
I missed your trademark "smiley face" at the end of the video. :-)
Great video on different logarithmic bases!
Sorry! 😔
Solution by insight
log _3 (9)=log _4(16)=2
a=8
Excelente. Excelent 🇧🇷🇧🇷🇧🇷
Answer a=3^log_4_ (7) -1
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.
Good thinking
@@ShortsOfSyber I mean you don't need any derivative and all to analyze in this case.
@@ShortsOfSyber you makes a simple prblm difficult 🤬
Keep up the great content.
Thanks, will do!
@@ShortsOfSyber is there anyway you can do some calculus integration techniques would be nice.
Your minimum point for your graph is a smiley face.
🙃
a = 8
X will be 2 and a will be 8 simply without too long process.