Lecture 4 : General Logarithms and Exponentials. log a x = lnx lna The algebraic properties of the natural logarithm thus extend to general logarithms, by the change of base formula log a 1 = 0; log a (xy) = log a (x) + log a (y); log a (x r) = rlog a (x): for any positive number a 6= 1 In fact for most calculations (especially limits, derivatives and integrals) it is advisable to convert
ial maths pure 2 ex3a - MyMathsCloud 0 25 x 2 2 1 1 16 0 25 16 1 b Let log a ax xa = a x = 1 ? log 1 a a 8 a i log 1 0 2 ii log 1 0 3 iii log 1 0 17 b Let log 1 a x xa = 1 x = 0 ? log 1 0 a
Worksheet 5. - University of Connecticut x2 2 3 p x x4 Properties of Logarithms Let a be a positive number such that a 6= 1, and let n be a real number If u and v are positive real numbers, then the following properties are true Logarithm with Base a Natural Logarithm 1 Product Property: log a (uv) = log a u+ log a v ln(uv) = lnu+ lnv 2 Quotient Property: log a u v = log a u log a v