Question

What are the Logarithm rules?

Answer 1

Logarithm rules are as follows:

$\ln$ is logarithm on base $e$.

• Log of power: It means the logarithm of a variable with an exponent is the product of the exponent and the logarithm of a variable.$\ln \left(x^y\right)=y\ln x$,
• Product rule: It means the logarithm of the product is the sum of the logarithm of each variable. $\ln \left(x.y\right)=\ln x+\ln y$, $x$ and $y$ are positive.
• Quotient rule: It means the logarithm of quotient is logarithm of the division and logarithm divisor.
  $\ln \left(\frac{x}{y}\right)=\ln x-\ln y$, $x$ and $y$ are positive.
• Log reciprocal: It means the logarithm of a variable with an exponent $-1$ is minus of logarithm of the variable. $\ln \left(x^{-1}\right)=\ln \left(\frac{1}{x}\right)=-\ln x$, $y$ is positive.
• Log of $1$: Logarithm of $1$ is zero. $\ln \left(1\right)=0$
• Log of $e$: Logarithm of $e$ is one. $\ln \left(e\right)=1$,