Logarithm of a power

\log_a x^k=k\log_a x

Result unit: — (liczba)

What it describes

The logarithm of a power is the exponent multiplied by the logarithm of the power's base.

a

base

x

positive number

k

exponent

The exponent “comes out in front of” the logarithm as a factor — exponentiation turns into multiplication.

Logarithms of powers and roots; solving equations.

Evaluate

\log_2 8^2

Substitution

2\cdot\log_2 8

Result

2\cdot3=6

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