Definition of a logarithm

\log_a b=c \iff a^c=b

Result unit: — (liczba)

What it describes

A logarithm is the exponent to which the base must be raised to obtain the argument.

a

base (

a>0,\ a\neq 1

)

b

argument (

b>0

)

c

value of the logarithm

A logarithm answers the question “to what power must the base be raised to obtain a given number?” It is the inverse operation of exponentiation.

Exponential equations, logarithmic scales (pH, decibels).

Evaluate

\log_2 8

Substitutionwe look for the exponent:

2^?=8

Result

\log_2 8=3

(since

2^3=8

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