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the hypotenuse of a right triangle is 20m if the difference between the length of the other sides is 4m find the sidesans apqx2 y2 202 x2 y2
example solve out each of the following
a lotus is 2m above the water in a pond due to wind the lotus slides on the side and only the stem completely submerges in the water at a distance of
first method draws back consider the following
example solve out example solve out
simpler methodlets begin by looking at the simpler method this method will employ the following fact about exponential functionsif b x b
in this section we will discussed at solving exponential equationsthere are two way for solving exponential equations one way is fairly simple
example evaluate log5 7 solutionat first notice that we cant employ the similar method to do this evaluation which we did in the first set of
the last topic that we have to discuss in this section is the change of base formulamost of the calculators these days are able of evaluating common
a dealer sells a toy for rs24 and gains as much percent as the cost price of the toy find the cost price of the toyans let the cp be
example simplify following logarithmslog4 x3 y5 solutionhere the instructions may be a little misleading while we say simplify we actually mean
for these properties we will suppose that x gt 0 and y gt 0logb xy logb x logb ylogb xy logb x - logb ylogb xr r
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