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:

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Prove.

Proof. Let

(1)       x = log_b N

or, equivalently,

(2)       b^x = N.

Taking log_a of both sides of (2), we have

(3)       x log_a b = log_a N

or

From (1) and (4) we get

End of Proof.

Prove.

Proof. Taking N = a and substituting into (5) we get

and since log_a a = 1, (6) becomes

End of Proof.