Change of Base Logarithm

hello my good people on this platform say thank you so much for the support that you're giving me please share the video remember to subscribe if you have not yet subscribed to my YouTube channel follow me on my Tik Tok my Facebook page this is camba Jacob all right so I'm going to show you how to use what we call change of base or bases okay so when you're dealing with logarithms you must understand that we've got bases and you can see this is the base and this is the base four is base two is base so now the way these logarithms work when you have got the same bases you can apply the rules of logarithms but if you can see nicely over here the bases are different which tells us that we can't work out we first need to balance the bases so how do you get to balance the bases on the logarithms so there is Formula that we follow so you can see when you've got log okay you can see log base let's say you've got base base of so if want to change this base I'm going to use this same formula say log okay sorry log base where want to take it want to take to Bas so log base where want to take it of okay over log okay the same base base over hopefully you can see here this will move with this over here with the new base the same new base it will now move with this we divide like this and this is the formula we use hopefully you will remember it okay so now let's try to apply this right here so that we can balance the bases so the way it will look it will look like this log okay want to take it to base two log base 2 over over okay you can see that over log okay base two the same base base two of four so you see what I've done I've changed this using change of Base formula and then say plus log base 2 of is = to 6 so now we've balanced the bases okay we've balanced the bases the only job that is remaining right now is to solve where I'm going to multiply throughout by this denominator want to get rid of the denominator minator so will multiply throughout by the denominator such that this one will will cancel will remain with log okay let me write down here the way it will be so when we multiply throughout this log Bas two of four throughout here here we are going to remain with log okay base two of X+ log base 2 2 of 4 * log base 2 of is equal to is equal to log base 2 of of four multiplied by six so this is what we are going to remain with hopefully you're able to see so since I'm running out of space let me copy this write here so we are here remember where we are don't get confused just follow me nicely so we are here log I'm just copying here base 2 of Plus log base 2 of 4 * DOT means times times log base 2 of is equal to log base 2 of 4 * 6 so I've just copied what is here so now from this stage we can now apply the rules of logarithms where we shall factor out this since this and this are common it's common is found here and here so we shall remain with it log base 2 of Open Bracket so here when we factor out we shall have 1+ log base 2 of 4 okay is equal to so I've just done the factorization here pick log 2 log base 2 of log base 2 of you bring it outside the brackets here you remain with the one here when it comes outside the brackets you remain with this which is right here and then the other side we have log base 2 of 4 * 6 so we divide by 1 + log base 2 of 4 because want to remain with this alone okay if you can see these brackets they mean multiplication so we can divide over 1 + log base 2 over 4 so here it will cancel we shall remain with the log we almost there log base 2 over log 2 log base 2 of 4 * 6 over 1 + log base 2 of 4 so so this is what we have we're at this stage so now from this stage you must be very careful there is only one thing that we need to perform here you can see when you've got base like this and you want to solve for which is here you write the is equal to you come and write what is here so let me write properly is equal to two you write this two you see is equal to two and all this thing which here which is this side must become the power so it will be Power log okay log base 2 of 4 * 6 over 1 + log base 2 over 4 so you can see you write is equal to 2 power all this thing which is right here it's more like the way you must be remembering it you must be remembering it in this way it two we will push this up it will become power and this is what we've written so if you punch on your calculator you'll see that the value of the value of will be equal to A6 if you don't have calculator you can leave it right here but if you have calculator you punch you find the value of to be equal to 16 thank you so much for watching this has been chamb Jacob please leave comment in the comment section below share the video let more people watch and tell your friends to tell their friends about this platform thank you and bye-bye