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WorkSHEET 5.2 Exponential and logarithmic functions 1 1 Evaluate log 3 . 3 Name: ____________________________ 1 log 3 3 log 3 3 1 log 3 3 1 2 Simplify log3 (18) + log3 (4) log3 (2). log 3 18 log 3 4 log 3 2 18 4 log 3 2 log 3 36 3 Simplify 5 log3 (8) 2 log3 (16) . 5 log 3 8 2 log 3 16 log3 8 log3 16 5 2 85 log3 2 16 log3 128 4 2 1 Simplify log 4 (27) log 4 (25) . 3 2 2 1 log 4 27 log 4 25 3 2 2 1 log 4 27 3 log 4 25 2 2 1 log 4 33 3 log 4 52 2 log 4 9 log 4 5 log 4 45 Maths Quest 11 Mathematical Methods CAS 2nd edition 1 WorkSHEET 5.2 Exponential and logarithmic functions 5 1 Simplify 4log10 x log10 3 x 2log x . 3 10 1 4log10 x log10 3 x 2log x 3 10 2 11 log10 x 4 log10 x 2 3 log10 x3 1 log10 x 4 log 10 x 6 log10 x 6 4 16 x x log10 6 x log10 x 6 Solve for x: log5 2 x 3 4 11 6 11 log10 x 6 log 5 (2 x 3) 4 2 x 3 54 2 x 3 625 2 x 628 x 314 7 Solve for x: log x (2) log x (128) 3 log x 2 log x 128 3 2 log x 3 128 1 x 3 64 4 3x 3 x4 Maths Quest 11 Mathematical Methods CAS 2nd edition 2 WorkSHEET 5.2 Exponential and logarithmic functions 8 Solve 2log3 ( x) log3 (6 x) 1. 2 log 3 x log 3 6 x 1 log 3 x 2 log 3 6 x 1 x2 log 3 1 6x x2 31 6x x 2 18 x x 2 18 x 0 x x 18 0 x 0 or x 18 x = 18 is the only solution (log 3 0 is not possible). 9 32 x 413 x Solve for x, correct to 3 decimal places: 32 x 413x log10 32 x log10 4 13 x 2 x log10 3 1 3 x log10 4 2 x log10 3 log10 4 3 x log10 4 2 x log10 3 3 x log10 4 log10 4 x 2 log10 3 3log10 4 log10 4 x log10 4 2 log10 3 3log10 4 x 0.218 Maths Quest 11 Mathematical Methods CAS 2nd edition 3 WorkSHEET 5.2 Exponential and logarithmic functions 10 Sketch the graph of y = 10x, and hence sketch the graph of y = log10 (x) on the same set of axes. The graph of y = 10x has a y-intercept of 1 and an asymptote at y = 0. The graph of y = log10 (x) has an x-intercept of 1 and an asymptote at x = 0. The graphs of y = 10x and y = log10 (x) are reflections of each other across the line y = x. Maths Quest 11 Mathematical Methods CAS 2nd edition 4