Website owner: James Miller
RULES OF EXPONENTS AND LOGARITHMS
Let a, b, p, q be any real numbers.
Rules of exponents.
Laws of logarithms.
Change of base:
________________________________________________________
Prove.
Proof. Let
(1) x = logb N
or, equivalently,
(2) bx = N.
Taking loga of both sides of (2), we have
(3) x loga b = loga N
or
From (1) and (4) we get
End of Proof.
Prove.
Proof. Taking N = a and substituting into (5) we get
and since loga a = 1, (6) becomes
End of Proof.
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