How to prove the logarithm product rule i.e. show that log_a(xy)=log_a(x)+log_a(y)
© The Maths Studio (themathsstudio.net)
Logarithms are mathematical functions that represent the exponent or index to which a base must be raised to obtain a given number. Logarithms have several laws that simplify the manipulation of these functions. Here are the fundamental logarithm laws:
1. *Product Rule:*
logₐ(xy) = logₐ(x) + logₐ(y)
This rule states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the individual numbers.
2. *Quotient Rule:*
logₐ(x/y) = logₐ(x) - logₐ(y)
The quotient rule states that the logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator.
3. *Power Rule:*
logₐ(xⁿ) = n × logₐ(x)
This rule states that the logarithm of a number raised to a power is equal to the exponent times the logarithm of the base.
4. *Change of Base Formula:*
logₐ(x) = logₕ(x) / logₕ(a)
This formula allows you to change the base of a logarithm. Common choices for h are 10 (common logarithm) or e (natural logarithm).
These laws are useful for simplifying logarithmic expressions, solving equations involving logarithms, and performing various mathematical manipulations involving logarithmic functions.
Watch video How to prove the logarithm product rule i.e. show that log_a(xy)=log_a(x)+log_a(y) online without registration, duration hours minute second in high quality. This video was added by user The Maths Studio 25 June 2020, don't forget to share it with your friends and acquaintances, it has been viewed on our site 199 once and liked it 2 people.