#1 Suppose ln(x+2)+ln(x-2)=ln(5) and the question is : "Find `x'". Is
the answer a number (and if so what number) or some expression
involving x?
#2 Suppose ln (x-3)=ln(x)-ln(3) {for all x}. Then it would be true
that ln22=ln25-ln3. But ln22=3.09; ln25=3.22;ln3=1.1 [YOU can use a
calculator!!]. But, 3.22-1.1=2.12 NOT 3.09. What is wrong!. You must
never forget the Barber who shaves all men and only those men who do
not shave themselves. And since we know there is no such Barber, what
does that say about ln(x+y)=lnx+lny?
#3 If x is a large negative number (e.g. –1000, -1000000000, your
call) is it possible that x^2+15x<c, where "c" is any positive
integer? Why or why not?
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