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February 24, 2011 Logarithmic Functions For every exponential function, there is a logarithmic function that is its inverse. Logarithmic Form Exponential Form 2 3 =9 log39 = 2 3-2 = 1/9 log (1/9) = -2 3 53 = 125 Write the exponential equation in logarithmic form: 53 = 125 4-2 = 1/16 7-u = w Write the logarithmic equation in exponential form: log 9 = 2 3 log (1/25) = -2 5 log 9 = m b February 24, 2011 Evaluate the expression without a calculator: log44 log416 log4(1/4) log4(1/16) log464 log4(1/64) Evaluate each expression. log5625 log9729 Think 5x = 625. The power must be bigger than 1. February 24, 2011 Evaluate each expression. log7(1/49) log4(1/64) x Think 7 = 1/49. The power must be negative to get a reciprocal. February 24, 2011 When a log and exponent have the same base and are applied back to back, they cancel each other. Evaluate the expression without a calculator: log13169 log450 13 logm22 m 4 log77-13 logbb1.7 Assignment: "The Meaning of Logarithms" worksheet Don't do #27, 31, or 36.