EXPONENTIAL AND LOGARITHMIC FUNCTIONS (Part-3)

─►Properties of Logarithms

• LOG of 1 is 0: Given the logarithmic function f(x) = LOG_ax, f(1) = 0.In other words

    LOG_a1 = 0 for any legitimate exponential base a.

• LOG_a of a is 1: Given the logarithmic function f(x) = LOG_ax, f(a) = 1.In other words,

    LOG_a a = 1 for any legitimate exponential base a.

• Product Rule for Logs: Given the logarithmic function f(x) = LOGax, f(UV) = f(U) + f(V).In other words,

    LOG_a(UV) = LOG_aU + LOG_aV for any legitimate exponential base a.

• Quotient Rule for Logs: Given the logarithmic function f(x) = LOG_ax, f(U/V) =

f(U) - f(V).In other words,

 for any legitimate exponential base a.

 • Power Rule for Logs: Given the logarithmic function f(x) = LOG_ax, f(x^N) =

N • f(x).In other words, LOGa(x^N) = N • LOG_ax.

 • Change of Base Rule for Logs: Given the logarithmic function f(x) = LOG_ax, it

is true, for any legitimate bases a and b, that