=CX 5. Graphical Behavior of the Log to the Base e (Natural Log) Function: a. Plot both the exponential function f(x)=e" and the logarithmic function g(x)= In x in Mathematica. (Notation: In Mathematica the notation for the natural log, In x is Log[x].) R b. Is f(x), the exponential function, increasing or decreasing? increasing faster and faster or slower and slower? c. Is g(x), the logarithmic function, increasing or decreasing? decycasing faster and faster or slower and slower? 6. We will complete this table together as a class: Rules of Exponents versus Rules of Logarithms Rules of Logarithms-Base 10 log(a-b) = log(a)+ log(b) log (=) = log(a)-log(6) log(a)= b.log(a) 10 x"x = X Rules of Exponents EX: X a+b +96 Ext 2+3 = x =x5 log(10")= On a separate sheet of paper, check the above rules by: a. choosing different values of a and b b. calculating both sides of the rule's equality, and c. checking to see if both sides are the same.