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Using logs to Linearise the Data The equation is y = ab x x12345678910 y111988777696154474238 This graph is NOT linear

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Using logs to Linearise the Data The equation is y = ab x log y = log(ab x ) log y = log a + logb x Using the addition rule log(AB) = logA + logB log y = log a + (xlogb) Using the drop down infront rule log y = (logb) x + loga Rearranging to match with y = mx + c x12345678910 y111988777696154474238 Take logs of both sides

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So make a new table of values x = x Y = logy Matching up : Y axis = log y gradient =m = logb x axis = x C = log a log y = (logb)x + loga Rearranging to match with y=mx + c

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Plot x values on the x axis and logy values on the y axis x12345678910 y111988777696154474238 logy2.051.991.941.891.841.791.731.671.621.58

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y = -0.0522x + 2.0973 The equation of the line is log y = logb x + loga gradient = log b = -0.0522 Matching up : y = mx + c C = log a = 2.0973 YmXc

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gradient = log b = -0.0522 To find b do forwards and back b log it = –0.0522 Backwards –0.0522 10 it b b = 10 –0.0522 = 0.8867

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y intercept = log a = 2.0973 To find a do forwards and back a log it = 2.0973 Backwards 2.0973 10 it a a = 10 2.0973 = 125.1

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The exponential equation is y = ab x y = 125.1×0.887 x

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Using the equation y = 125.1×0.887 x If x = 5.5 find y y = 125.1×0.887 5.5 = 64.7 Check if the answer is consistent with the table x = 5.5 find y y = 64.7 which is consistent with the table x12345678910 y111988777696154474238

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Using the equation y = 125.1×0.887 x If y = 65 find x 65 = 125.1×0.887 x log65 = log(125.1×0.887 x ) = log(125.1)+log(0.887 x ) = log(125.1)+xlog(0.887) Take logs of both sides Using the addition rule log(AB) = logA + logB Using the drop down infront rule

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log 65 = log(125.1)+xlog(0.887) Forwards and backwards x ×log0.887 +log 125.1 = log65 log65 –log 125.1 ÷log0.887 = x x = 5.46 x = 5.46 which is consistent with the table Check if the answer is consistent with the table y = 65 find x x12345678910 y111988777696154474238

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Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

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