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

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 x y Take logs of both sides

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

Plot x values on the x axis and logy values on the y axis x y logy

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

gradient = log b = To find b do forwards and back b  log it = – Backwards –  10 it  b b = 10 – =

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

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

Using the equation y = 125.1×0.887 x If x = 5.5 find y y = 125.1× = 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 x y

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

log 65 = log(125.1)+xlog(0.887) Forwards and backwards x  ×log0.887  +log = log65 log65  –log  ÷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 x y