let's do some math for fun and this is about logarithms in the exponent and then we are also
dealing with the cubic so you see this is the equation I were to solve and with the X right
here right here and right here has three different places right hmm how can I approach this we are
the main thing here is that we have the eggs in the log and this is in the exponent right and
usually you put the X is you know in the exponent somewhere here we should take the log on both
sides so that we can bring the exponent to the front and let me do that and because here we have
log base 2 already let's match that base so first let me take log base 3 on the left hand side of
course we have to do the same thing on the right hand side so we see that for this this is just a
power we can bring that to the front and we will have this which is log base 3 of x times we have
another log base 3 of X so let me put this down red good and this is equal to we have log base 3
of 81 and this is a multiplication right 81 times X to the third power and we know log of a product
is the sum of two logs we can break this apart as log of 3 log base 3 of 81 plus log base 3 of
X to the third power okay now what can we do next well here we know this is just a regular number
log base 3 of 81 you ask yourself Street to what power is h1 3 to the fourth power is 81 right so
we know this is going to be a 4 ok so now we have to work on this and we see that we can bring the
power street right here and then bring up to the front that's what we have let me rewrite this in
a better way you see that this times that is just log base 3 of X in the parenthesis and then to a
second power so I'll write this as log base 3 of X like this and then take this way start with the
2nd power by in this case be sure to not bring the tool to the front because we're not saying
x times X inside this is right this is X to the third power we can bring the street to the front
but this right here it means log base 3 times log base 3 we cannot bring the 2 to the front
a peekaboo step all right this is equal to this is 4 and then we have the 3 in front so we have
plus 3 and this is another log base 3 of X that we have right here right so ok break it up this
for you guys right now you see we have started to the second power and this and that match in fact
this is just a quadratic equation right in terms of log base 3 so you can do it whichever way that
you want to do a lot of people like to do it with another variable I will show you guys like that as
to log base B of X just this way I can write this down as Y Square and this is equal to 4 plus this
is 3 times y so quadratic equation in terms of Y now solve it easy right y square doing this and
that will definitely to a minus 3 y minus 1 this is equal 0 factor it easy right this is y minus
4 times y plus 1 equals to 0 solve it easy right you know y minus 4 equals to 0 y plus 1 equal to 0
first answer right here why it's equal to 4 second answer you know Y is equal to negative 1 that we
don't care about why we care about X huh so right here you will have log base 3 of x equals to 4
and this is log base 3 of x equals to negative 1 what we do we take 3 to that power we take 3 to
that power so that they cancel once again we'll pretend both sides are the exponents so this is
the same as a 3 to this power and 3 to the power so finally we get X equal to 3 to the fourth power
is 81 first answer and you plug this back into the original and let me tell you it works secondly
we do the same thing through to this power and through to that power cancel cancel x equals to
3 to the negative 1 which we know is 1 over 3 and you should also check this answer right here right
here right you work as well this is really nice this is the sole realty side equation I love it