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The definitions and properties of logarithms can be used to solve equations in which either powers or logs appear.It is important to remember that y=logax is defined only for x>0. Some equations will give roots that are less than zero. These roots must be checked in the original equation to see if x is a valid answer. If not, these roots are inadmissible/extraneous.Example 1Solve for x. State any restrictions on the variable as part of your solution.log42x+6=3b) log6x+3+log6(x-2)=1log5x2-21x=25Example 2Solve. State any restrictions on the variable. Answer to two decimals if applicable.b) d) e) f) h) j) k) 2log4(x)-log44x+3=-1l) 5x-4=3(42x+1)m) log3(x-1)=log3x2-log3(x+3)Example 3Algebraically, determine all points of intersection of the two functionsfx=log2(2x-2)gx=5-log2(x-1)39909759652000Also, sketch a graph of both functions to verify. ................
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