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Finding Exponential Equations Using Logs: A Straightforward Approach

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ranee
18 diapositives · 307 Views · Sep 10, 2014

This guide explores how to find exponential equations using logarithms in R. We start by transforming data points into a logarithmic format, then derive the slope (m) and intercept (c) of the line, leading to the equation log(R) = m log(t) + c. We'll also convert the logs to base 10 where needed for simplification, ensuring no logs remain in the final equation. Using example points and the addition rule, we demonstrate the step-by-step process of eliminating logs and obtaining the final exponential form.

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Finding Exponential Equations Using Logs: A Straightforward Approach
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  1. Finding Exponential Equations (using logs)

  2. R Not very straight!  x x x x x x x t

  3. R Exponential x Equation? x x x x x x t

  4. log R find equation with log R and log t in form log R = m log t + c x x x x x x x log t

  5. gradient log R need two points on line x (4 , 34) x m = 34 - 6 = 28/4 x 4 – 0 x = 7 x y = 7x + 6 x x log R = 7 log t + 6 6 do not want logs in equation log t

  6. log R = 7 log t + 6 logless! ? want to change 6 → log10........ log statement log10 x = 6 translation x = 106 equation becomes log10 106 log R = 7 log t + no need to always write 10 still some work to do!

  7. log R = 7 log t + log106 to get rid of logs want log…. = log…. Time for some log rules

  8. log R = 7 log t + log106 Neat Wee Rule log R = log t7 + log106 Addition Rule (t7 X 106) log R = log R = 1000000t7

  9. Finding Exponential EquationsUsing Logs Tactics Get straight line equation with logs Change everything to logs Get rid of the logs!!

  10. log R find equation with log R and log t in form log R = m log t + c x x x x x x x log t

  11. Find Gradient log R need two points on line x (13 , 34) x m = 34 - 8 = 26/13 x 13 – 0 x = 2 x y = 2x + 8 x x log R = 2 log t + 8 8 log t

  12. log R = 2 log t + 8 logless! want to change 8 → log10? log statement log10 x = 8 translation x = 108 equation becomes log R = 2 log t + log 108 no need to always write 10

  13. log R = 2 log t + log108 to get rid of logs want log…. = log…. Neat Wee Rule log R = log t2 + log108 Addition Rule log log (t2 X 108) R = Eliminate Logs (t2 X 108) R = R = 100000000t2

  14. log R Equation log R = mt + c x x x x x x x t

  15. log R x (6 , 7) x m = 7 - 4 = 3/6 x 6 – 0 x = 0.5 x y = 0.5x + 4 x x log R = 0.5t + 4 4 t

  16. log R = 0.5t + 4 logless! want to change 4 → log10 same for 0.5t log statement log10 x = 4 log10 x = 0.5t translation x = 104 x = 100.5t equation becomes log R = log 100.5t + log 104

  17. log R = log 100.5t + log 104 Addition Rule log log (100.5t X 104) R = Eliminate Logs R = (100.5t X 104) R = 10000 X 100.5t 100.5 = 3.2 R = 10000 X 3.2t R = 10000 (3.2)t

  18. Annoying First Part of Question Sort of Thing If y = abt Show that the relationship between log y and log b is linear log y = log abt reverse addition rule log y = log a + log bt Neat Wee Rule log y = log a + t log b log y = t log b + log a eh? log both sides like y = mx + c → linear