Logarithm Power Rule | Math Rules | Equation Encyclopedia

Q: What is an example of the Logarithm Power Rule?

\log_2(8^3) = 3 \log_2(8) = 3 \cdot 3 = 9

Q: What should I remember about the Logarithm Power Rule?

This rule is valid for any positive base $b \neq 1$, any positive number $x$, and any real number $c$. It is derived from the definition of logarithms and the exponent rule $(b^y)^c = b^{yc}$.

The rule

Description

The logarithm power rule states that the logarithm of a number raised to an exponent is equal to the product of the exponent and the logarithm of the number. This rule is crucial for simplifying logarithmic expressions and is a fundamental property in algebra.

See it in action

Examples

1

$lo g_{2}$ (8^3) = 3 $lo g_{2}$ (8) = 3 $\cdot$ 3 = 9

2

ln (x^{5}) = 5 ln (x)

Good to know

Key Facts

This rule is valid for any positive base $b \neq = 1$ , any positive number $x$ , and any real number $c$ .
It is derived from the definition of logarithms and the exponent rule $(b^{y})^{c} = b^{y c}$ .

Common questions

Frequently Asked Questions

The logarithm power rule states that the logarithm of a number raised to an exponent is equal to the product of the exponent and the logarithm of the number. This rule is crucial for simplifying logarithmic expressions and is a fundamental property in algebra.

$lo g_{2}$ (8^3) = 3 $lo g_{2}$ (8) = 3 $\cdot$ 3 = 9

This rule is valid for any positive base $b \neq = 1$ , any positive number $x$ , and any real number $c$ . It is derived from the definition of logarithms and the exponent rule $(b^{y})^{c} = b^{y c}$ .