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there are several quantities out there within the world which are governed at least for a short time period by the
a pole has to be erected at a point on the boundary of a circular park of diameter 13m in such a way that the differences of its distances from two
example we are investing 100000 in an account that earns interest at a rate of 75for 54 months find out how much money will be in the account ifa
in this last section of this chapter we have to look at some applications of exponential amp logarithm functionscompound interestthis first
example solve following equations2 log9 radicx - log9 6x -1 0solution along with this equation there are two logarithms only in the equation thus
a teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left over when he increased
the positive value of k for which x2 kx 64 0 amp x2 - 8x k 0 will have real roots ans x2 kx 64 0rarr b2 -4ac gt 0k2 - 256 gt 0k gt 16 or k
now we will discuss as solving logarithmic equations or equations along with logarithms in them we will be looking at two particular types of
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