PMath 12
Ch. 2 Laws and Rules of Logarithms
Definition of a Log
if... ay = x then... loga x = y
if... ey = x then... loge x = y
but... logex = ln x therefore ln x = y where ln e = 1
( ln is referred to as a natural log )
Law of Logarithms for Powers
logax n = n logax x > 0, a > 0, a ≠ 1
Change of Base Rule
logab = log b
log a
Law of Logarithms for Multiplication
logaxy = logax + logay x > 0, a > 0, a ≠ 1
Law of Logarithms for Division
logax/y = logax −logay x > 0, a > 0, a ≠ 1
Some handy cancellation equations... (try to make sense of why they work)
loga(ax) = x alogax = x ln(ex) = x eln x = x
PMath12 - Mr. R. Basi
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