Course Number Section 5.5 Bases Other Than e and Applications Instructor Objective: In this lesson you learned the properties, Date derivatives, and antiderivatives of logarithmic and exponential functions that have bases other than e. (Pages Other than e What you should learn How to define If is a positive real number (a 1) and is any real number, a x exponential functions that material to decay then the exponential function to the base is denoted by a ax and is defined by = . If = 1, then ax e(ln a y a)x 1x 1 is a constant function . = = . In a situation of radioactive decay, is the number half-life have bases other than e of years required for half of the atoms in a sample of radioactive If is a positive real number (a 1) a and is any positive real x number, then the logarithmic function to the base is denoted a by loga and is defined by loga 1/(ln ln . = x x a) x Complete the following properties of logarithmic functions to the base a. loga 1 = 0 loga (xy) = loga + loga x y = loga xn n x x loga = loga loga y x y State the Properties of Inverse Functions = if and only if = loga y ax x y = for > 0 aloga x x x loga = for all ax x, x
Section 5.5 Bases Other Than e and Applications Objective: In this lesson you learned the properties, derivatives, and antiderivatives of logarithmic and exponential functions that have bases other than e. Other than e (Pages Course Number Instructor Date What you should learn How to define If a is a positive real number (a 1) and x is any real number, exponential functions that then the exponential function to the base a is denoted by ax and is defined by ax = e(ln a)x . If a = 1, then y = 1x = 1 is a constant function . In a situation of radioactive decay, half-life is the number of years required for half of the atoms in a sample of radioactive material to decay . have bases other than e If a is a positive real number (a 1) and x is any positive real number, then the logarithmic function to the base a is denoted by loga x and is defined by loga x = 1/(ln a) ln x . Complete the following properties of logarithmic functions to the base a. loga 1 = 0 loga (xy) = loga x + loga y xn = n loga x x loga y = loga x loga y State the Properties of Inverse Functions y = ax if and only if x = loga y aloga x = x for x > 0 loga ax = x, for all x
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