Logarithm of a product

\log_a(xy)=\log_a x+\log_a y

Result unit: — (liczba)

What it describes

The logarithm of a product is the sum of the logarithms of its factors.

a

base

x, y

positive numbers

The logarithm turns multiplication into addition — this was the principle behind old slide rules.

Simplifying logarithms of products, splitting them into a sum.

Evaluate

\log_2(4\cdot8)

Substitution

\log_2 4+\log_2 8

Result

2+3=5

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