Power Laws of Logarithms

Quantity and/or base quantity of logarithmic terms can be expressed in exponential form to find the values of logarithm of quantities. Due to the involvement of exponents in logarithms, the logarithmic identities are simply called as power rules of logarithms.

There are three power rules in logarithms and they are used as formulas in logarithmic mathematics to find the values of logarithmic terms easily.

Power Rule of Logarithms

Logarithm of a quantity in exponential form is equal to the product of exponent and logarithm of base of exponential term.

$\large \log_{b}{m^x} \,=\, x\log_{b}{m}$

Base Power Rule of Logarithms

Logarithm of a quantity to a base in exponential form is equal to the quotient of logarithm of quantity by the exponent of base quantity in exponential form.

$\large \log_{b^y}{m} \,=\, \Big(\dfrac{1}{y}\Big)\log_{b}{m}$

Double Power Rule of Logarithms

Logarithm of a quantity in exponential form to a base in exponential form is equal to product of quotient of exponent of quantity by the exponent of base quantity and logarithm of quantity.

$\large \log_{b^y} m^x = \Big(\dfrac{x}{y}\Big) \log_{b} m$

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