Exponentials and logarithms

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exponential functions f(x) = ax always go through I on x-axis tends towards 0 as x decreases graphs of their gradient functions are similar to shape of the actuall function f(x) f'(x) between a= 2 and a=3 → graphs are the SAME Lo number given as e f(x)= ex then f'(x) = ex f(x) = ekx, then f'(x) = kekx " logarithms logan = x E means = x So f'(x) = Kf(x) logax + logay = loga xy loga x - logay = loga (1) loga (x²) клодах ax=n natural logarithms inex You can take logs of both sides f(x) = g(x logf(x) = logg(x) constant you can turn equations into linear data y = axh logy = logax" logy = loga + logxn logy = loga + nlogx → plot logy against logx y=/ex -multiplication law. division law. power law eg 3²=9 so log 39 = 2 Ly=x y=lnx e²x+3 = = 7 also Togaa = 1 loga=0 2x = ln 7-3 x = logal) = logalx") = -logax 2x+3 une ²x³ = ln 7° 2x+3 = Un7 2/17 - 12/22 Loas of both sides MIXED EXERCISES 1) a) y = 2* y= 2-x = (2-¹)² = ² 2) a) loga (²a) = Loga p² + loga q 2 loga P + loga q 3) a) p = loyalb : 몹 = 410992 Logą2 4) a) 4x = 23 x Log4 = log23 x= 10923 1094 5) a) u = 2x 1:4² = 4* b) y=5e²-1 y = -1 goes through 5 2x+1=2 x 2¹ = 2u - 4* - 2x+1 -15=0 = U² - 2U-15=0 b) P=logg16 b) loga (Pq) = 5 loga (P²q₂) = 9 loga P + logaq = 5 2 logap...

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