5.2 Properties of Exponents and Power Functions Product Property of Exponents a m *a n = a m+n Quotient Property of Exponents a m /a n = a m-n Definition of Negative Exponents a -n = 1/a n or (a/b) -n = (b/a) n Zero Exponents a 0 =1 Power of a Power Property (a m ) n =a mn Power of a Product Property (ab) m =a m b m Power Property of Equality If a=b, then a n =b n Common Base Property of Equality If a n =a m, and a doesn’t equal 1, then n=m Exponential Function The general form of an exponential function is y=ab x where a and b are constants and b>0 Power Function The general form of a power function is y=ax n where a and n are constants

5.3 Rational Exponents and Roots Definition of Rational Exponents The power of a power property shows that a m/n =(a 1/n ) m and a m/n =(a m ) 1/n Point-Ratio Form If an exponential curve passes through the point (x 1, y 1 ) and the function values have ration b for values of x that differ by 1, the point-ratio form of the equation is y= y 1 * b x-x1

5.6 Logarithmic Functions Definition of Logarithm For a>0 and b>0, log b a =x is equivalent to a=b x Logarithm Change-of-Base Property log b a=log a/ log b, where a>0 and b>0

5.7 Properties of Logarithms Properties of Exponents and Logarithms For a>0, b>0 and all values of m and n, these properties are true: Definition of Logarithm If x=a m, then log a x=m Product Property a m *a n = a m+n or log a xy=log a x + log a y Quotient Property a m /a n =a m-n or log a x/y=log a x-log a y Power Property log a x n =n log a x Power of a Power Property (a m ) n = a mn Power of a Product Property (ab) m =a m b m Power of a Quotient Property (a/b) n =a n /b n Change-of-Base Property log a x=log b x/log b a Definition of Negative Exponents a -n =1/a n or (a/b) -n = (b/a) n