Log168 log 8 log 16įinding Inverses of Exponential and Log Equations Switch x and y. Typing Logs into Calculator Logab = Log381 = log123 = 21. Recall that if logx5 = logxy then 5=y logx25 = 2 then 25 = x2 Condense logs to just ONE LOG on each side and then solve by log=log or log = # 13) log45 + log4x = log460 24) log2(x+4) – log2(x-3)= 3 Log45x = log460 5x = 60 x = 12 CHECK answer! No exponents! Bottom logs get ‘-’ Expand the following log: log log x4 – log 3 – log m2 4logx – log3 – 2logm Expand the following log: log log 圓 – log 3 – log m2 3logy – log3 – 2logm Minus logs, minus logs, divide them Log of 1 is zero, and can’t take log of negative.Ĭondensing Logs -logs go on bottom! Write as one log: 3logx + 2log y – 1/2log 9 – 3logm logx3 + log y2 – log 91/2 – log m3 logx3 + log y2 – log 3 – log m3 log Write as one log: -4logx - 2log y – 1/3log 64 – 3logm -logx4 - log y2 – log 641/3 – log m3 -logx4 - log y2 – log 4 – log m3 logĮxpanding Logs. Log6418 = m 128 = 64m 27 = 26m 7 = 6m 7/6 = m 7/6Ī3a5 = a3+5 loga3 + loga5 = loga(3*5) (a3)5 = a3*5 5loga3= loga35 a5 = a5-3 a3 loga5 – loga3 = loga (5/3) a0 = 1 Loga1=0 ax is always positive Loga(~) ~ is always positive!! Adding logs, Adding logs, multiply them A number in front of log becomes the exponent. Occassionally, you might want to put a “m” into the problem to make it easier to simplify 10. Ex: 10log4 4 because 10 and log10cancel.
Ex: log3 9 is read as 3 to what power is 9 2.Logab is written as ‘a’ to what power is ‘b’.
Ln follows log rules 13: ex =b then ln (b) = x Ex: ex+3= 5 x+3 = ln 5 x = ln 5 – 3 14: a = ln(x) then ea = x Ex: 5 = ln(x+3) e5 = x + 3 15: Ln(x) = ln(y) then x = y Ex: ln(x+1) = ln 5 x + 1 =5 x = 4 16: ex = ey then x = y Ex: ex = e5 x = 5 17: Ln em = m Ex: ln (e)4 4 18: elnm = m Ex: eln4 4 19: logam can be written as log(m)log(a) Ex: log38 on calculator log (8)/log(3) Rules of Logs
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