475 4.3 Logarithmic Functions Given that log10 2 ≈0.3010 and log10 3 ≈0.4771, find each logarithm without using a calculator. See Example 7. 93. log10 6 94. log10 12 95. log10 3 2 96. log10 2 9 97. log10 9 4 98. log10 20 27 99. log10 230 100. log10 361/3 Use properties of logarithms to rewrite each function, then graph. See Examples 3–5. 101. ƒ1x2 = log2341x - 324 102. ƒ1x2 = log3391x + 224 103. ƒ1x2 = log3 x + 1 9 104. ƒ1x2 = log2 x - 1 2 Concept Check Use the properties of inverses to determine whether ƒ and g are inverses. 105. ƒ1x2 = 5x, g1x2 = log 5 x 106. ƒ1x2 = a 1 5b x , g1x2 = log1/5 x 107. ƒ1x2 = log2 x + 1, g1x2 = 2x-1 108. ƒ1x2 = 4 log 3 x, g1x2 = 3x/4 109. ƒ1x2 = log41x + 32, g1x2 = 4x + 3 110. ƒ1x2 = log 10 2x, g1x2 = 102x Concept Check Write an equation for the inverse function of each one-to-one function given. 111. ƒ1x2 = 3x 112. ƒ1x2 = a 1 3b x 113. ƒ1x2 = 5x + 1 114. ƒ1x2 = 4x+2 115. ƒ1x2 = log 10 x 116. ƒ1x2 = log1/10 x (a) Make a scatter diagram of the data. (b) Which type of function will model this data best: linear, exponential, or logarithmic? –2 –1.5 –1 –0.5 0 0.2 0.4 0.6 0.8 1 x y y = 3x 119. Prove the quotient property of logarithms: loga x y = loga x - loga y. 120. Prove the power property of logarithms: loga x r = r log a x. 118. Concept Check Use the graph to estimate each logarithm. (a) log3 0.3 (b) log3 0.8 Solve each problem. 117. (Modeling) Interest Rates of Treasury Securities The table gives interest rates for various U.S. Treasury Securities on January 2, 2018. Time Yield 3-month 1.44% 6-month 1.61% 2-year 1.92% 5-year 2.25% 10-year 2.46% 30-year 2.81% Data from U.S. Department of the Treasury.
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