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the sum of areas of two squares is 468m2 if the difference of their perimeters is 24cm find the sides of the two squaresans let the
properties of logarithms1 logb1 0 it follows from the fact that bo 12 logb b 1 it follows from the fact that b 1 b 3 logb bx x
example evaluate each of the following logarithmsa log1000 b log 1100 c ln1e d ln radicee log34 34f log8 1solutionin order to do the
example evaluate following logarithmslog4 16solutionnow the reality is that directly evaluating logarithms can be a very complicated process
logarithm formin this definition y logb x is called the logarithm formexponential formin this definition b y x is called the exponential
logarithm functionsin this section now we have to move into logarithm functions it can be a tricky function to graph right away there is some
1abx 1a1b1x ab ne 0ans 1abx 1a1b1xgt 1abx -1x 1a 1brarr x - a b xxa b x a b abrarrabxabxab0rarrxabxab0rarrx2
exponential functionas a last topic in this section we have to discuss a special exponential function actually this is so special that for
properties of f x b x1 the graph of f x will always have the point 01 or put another way f0 1 in spite of of the value of b2 for every
definition of an exponential functionif b is any number like that b 0 and b ne 1 then an exponential function is function in the
solve by factorizationx2 aab abax1 0x2 aab abax1gt x2 aab x abax aab abagt xxaab abaaaab 0gt x -aab x -aba ab ne
in this section we will look at exponential amp logarithm functions both of these functions are extremely important and have to be understood
find out the partial fraction decomposition of each of the following8x2 -12 x x2 2 x - 6solutionin this case the x which sits in the front is a
example find out the partial fraction decomposition of following 8x - 42 x2 3x -18solutionthe
quadratic equations for the things of this world cannot be made known without a knowledge of mathematicssolve
this section doesnt actually have many to do with the rest of this chapter but since the subject required to be covered and it was a fairly short
the population of the village is 5000 if in a year the number of males were to increase by 5 and that of a female by 3 annually the population
a cyclist after riding a certain distance stopped for half an hour to repair his bicycle after which he completes the whole journey of 30km at half
synthetic division tablein a synthetic division table perform the multiplications in our head amp drop the middle row only writing down the third row
process for finding rational zeroes1 utilizes the rational root theorem to list all possible rational zeroes of the polynomial p x 2 evaluate the
finding zeroes of a polynomialthe below given fact will also be useful on occasion in determining the zeroes of a polynomialfactif p x is a
determine a list of all possible rational zeroeslets see how to come up along a list of possible rational zeroes for a polynomialexample find
for starters it will let us to write down a list of possible rational zeroes for a polynomial and more significantly any rational zeroes of a
example prove that the roots of the below given polynomial satisfy the rational root theoremp x 12x3 - 41x2 - 38x 40 x - 4 3x - 2 4x
if the rational number x b c is a zero of the nth degree