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write following in terms of simpler logarithms a log3 9 x4 radicysolutionlog3 9 x4 radicy log shy3 9x4 - log y 12log shy3 9 log
properties1 the domain of the logarithm function is 0 infin in other terms we can just plug positive numbers into a logarithm we cant
logarithm functions in this section well discuss look at a function which is related to the exponential functions we will learn logarithms in this
definition of natural exponential function the natural exponential function is f x ex where e 271828182845905 hence since e gt 1 we also
natural exponential function there is a extremely important exponential function which arises naturally in several places this function is called as
general approach of exponential functions before getting to this function lets take a much more general approach to things lets begin with b 0 b ne
solve 5x tan 8x 3x solution firstly before we even begin solving we have to make one thing clear do not cancel an x from both sides whereas
solve 8 cos2 1 - x 13 cos1 - x - 5 0 solutionnow as specified prior to starting the instance this quadratic does not factor though that doesnt
solve 4 sin 2 t - 3 sin t 3 1 solutionbefore solving this equation lets solve clearly unrelated equation4x2 - 3x 1 rarr 4x2 - 3x -1 4x 1
standard trig equation now we need to move into a distinct type of trig equation all of the trig equations solved to this point were in some way more
solving trig equations with calculators part ii since this document is also being prepared for viewing on the web we split this section into two
solve sin 3t 2 solutionthis example is designed to remind you of certain properties about sine and cosine recall that -1 le sin theta le 1 and
solve sin alpha 7 0 solutionby using a unit circle it isnt too difficult to see that the solutions to this equation arealpha 7 0 2
solve cos 4 theta -1 solutionthere actually isnt too much to do along with this problem however it is different from all the others done to
decimal representations of some basic angles as a last quick topic lets note that it will on occasion be useful to remember the decimal
solving trig equations with calculators part i the single problem along with the equations we solved out in there is that they pretty much all had
our objective is solve the following fourth-order bvp axu f x u0 u10 u0 u10 a give the variational formulation
euler equations - series solutions to differential equations in this section we require to look for solutions toax2 yprimeprime bxyprime cy
once we get out of the review we are not going to be doing a lot with taylor series but they are a fine method to get us back into the swing of
given f x 3x - 2 determine f -1 x solutionnow already we know what the inverse to this function is as already weve done some
finding the inverse of a function the procedure for finding the inverse of a function is a rather simple one although there are a couple of steps
definition of inverse functions given two one-to-one functions f x and g x if f o g x x and g o f x xthen we say that f x
one-to-one function a function is called one-to-one if not any two values of x produce the same y mathematically specking this is the same as
inverse functions in the last instance from the previous section we looked at the two functions f x 3x - 2 and g x x 3 23 and saw that f o
function composition the next topic that we have to discuss here is that of function composition the composition of fx amp gx is f o g x f g x