Logarithm

The 1797 Encyclopædia Britannica explanation of logarithms

Schematic depiction of a slide rule. Starting from 2 on the lower scale, add the distance to 3 on the upper scale to reach the product 6. The slide rule works because it is marked such that the distance from 1 to x is proportional to the logarithm of x.

In mathematics, the logarithm is the inverse operation to exponentiation. That means the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. In simple cases the logarithm counts repeated multiplication. For example, the base $10$ logarithm of $1000$ is $3$ , as $10$ to the power $3$ is $1000$ ( $1000 = 10 \times 10 \times 10 = 10$ ); the multiplication is repeated three times. More generally, exponentiation allows any positive real number to be raised to any real power, always producing a positive result, so the logarithm can be calculated for any two positive real numbers $b$ and $x$ where $b$ is not equal to $1$ . The logarithm of $x$ to base $b$ , denoted $log b (x)$ , is the unique real number $y$ such that

单词	Base of a logarithm
释义	Base of a logarithm 英语百科 Logarithm In mathematics, the logarithm is the inverse operation to exponentiation. That means the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. In simple cases the logarithm counts repeated multiplication. For example, the base $10$ logarithm of $1000$ is $3$ , as $10$ to the power $3$ is $1000$ ( $1000 = 10 \times 10 \times 10 = 10$ ); the multiplication is repeated three times. More generally, exponentiation allows any positive real number to be raised to any real power, always producing a positive result, so the logarithm can be calculated for any two positive real numbers $b$ and $x$ where $b$ is not equal to $1$ . The logarithm of $x$ to base $b$ , denoted $log b (x)$ , is the unique real number $y$ such that
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Base of a logarithm

Logarithm