Today in Precalculus Go over homework Notes: Common and Natural Logarithms Homework

Common Logs Base 10 is known as the common log, if no base is written in a log, it is assumed to be base 10 example: x = log 5 is the same as x = log 10 5 This is one of two bases we can use our calculators Example: x = log 260 = 2.415

Properties of Common Logs log10=1 since 10 1 = 10 log10 x =x since 10 x = 10 x log1=0 since 10 0 = 1 10 logx = x since logx = logx

Solving simple equations with Common Logs Solve: 10 x = 3.7 x=log3.7 x= Solve: logx = –1.6 x = x= 0.025

Natural logs Used for the natural base, e, and can also be calculated with calculators. Inverse of e x Abbreviated ln Example: x = ln14.32 = 2.662

Properties of Natural Logs lne=1 since e 1 = e lne x =x since e x = e x ln1=0 since e 0 = 1 e lnx = x since lnx = lnx

Solving simple equations with Natural Logs Solve: lnx = 3.45 x=e 3.45 x= Solve: e x = 6.18 x = ln6.18 x= 1.821

Homework Page 308: 7-35 odd