Only formulas and properties of logarithms

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The value of a logarithm corresponds to the exponent of a given base equal to a positive number “b” in the base “a”, which must also be positive and different from 1.

For any a > 0, a ≠ 1 and b > 0, x > 0, y > 0 the following properties of logarithms hold.

properties of logarithms
aloga b = b

loga 1 = 0

loga a = 1

loga 1a = -1

logax · y = loga x+loga y

loga xy = logax-loga y
loga 1y = -loga y

loga xn = n loga x

logaxn = loga xn

logan x = loga xn,   при n ≠ 0

loga x = logac xc

loga x = logb xlogb a

loga x = 1logx a

loga x′ = 1x ln a
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