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Date Class Name Date Class Name Reteach Reteach Logarithmic Functions Logarithmic Functions (continued) The logarithmic function is the inverse of the exponential function. Use this A logarithm is another way to work with exponents in equations. If b" = a, then log, a = X. fact to graph the logarithmic function. If b to the x power equals a, Graph a function and its inverse. then x is the logarithm of a in base b Graph / (x) = 0.5- using a table of values, -2 -1 o 2 Use the definition of the logarithm to write exponential equations in logarithmic form and to 4 2 1 05 0.25 write logarithmic equations in exponential form. Exponential Form Logarithmic Form Write the inverse function, 3' =81 base, b = 3 log, 81 = 4 (x) =log. . x exponent, x = 4 x and f (x) switch value, a = 81 The base is 0.5 places in the function and its inverse Logarithmic Form Exponential Form log, 125 = 3 base, b = 5 5- 125 exponent, x = 3 value, a = 125 X 2 1 0.5 0.25 f ' (x ) 2 1 0 If no base is written for a logarithm, the base is assumed to be 10. Example log 100 = 2 because 1 02 = 100 Remember, the graph of the inverse is the reflection of the onginal function Assume the base is 10. across the line y = x Write each exponential equation in logarithmic form. 17-49 2. 6 -216 3. 2"= 32 Complete the tables. Graph the functions. b =7, x=2, a =49 b= X= a= 7 ((x) = 4" 2 1 0 1 2 Write each logarithmic equation in exponential form. 1(x) 16 4. log, 729 - 3 5. 10g, 64 = 6 6 log 1000 - 3 b=9, x=3, a=729 b= X= (x) - log. x X 1 (x) ability of live inatractor Hot Mcdougal Algebra 2 Hou MeDeligal Abating