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there is a third method that well be looking at to solve systems of two equations but its a little more complicated and is probably more useful for
now lets move into the next technique for solving systems of equations as we illustrated in the example the method of substitution will
example solve following systemsa 3x - y 7 2x 3 y 1solutionthus it
methods for solving systemswe will be looking at two methods for solving systems in this sectionmethod of substitutionthe first method is known as
example if 8 times1014 joules of energy is released at the time of an earthquake what was the magnitude of the earthquakesolutionthere
earthquake intensitycommonly the richter scale is utilized to measure the intensity of an earthquake there are several different ways of computing
example the growth of a colony of bacteria is provided by the
there are several quantities out there within the world which are governed at least for a short time period by the
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
now we will discuss as solving logarithmic equations or equations along with logarithms in them we will be looking at two particular types of
example solve out each of the following
first method draws back consider the following
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
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
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