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A useful property of logarithms states that the logarithm of a product of two quantities is the sum of the logarithms of the two factors. In symbols, logo(XY)=logo(x)+logo(y). (x y) = log b (x) + log b
A useful property of logarithms states that the logarithm of a product of two quantities is the sum of the logarithms of the two factors. In symbols, logo(XY)=logo(x)+logo(y). (x y) = log b (x) + log b
When we take the logarithm of both sides of ELN(XY)=ELN(x)+LN(y), we obtain LN(ELN(XY))=LN(ELN(x)+LN(y)). The logarithms and exponential cancel each other out (equation (4)), giving our product rule for logarithms, LN(XY)=LN(x)+LN(y).
0:24 5:03 Suggested clip Sum of logarithms with same base | Logarithms | Algebra II | Khan YouTubeStart of suggested client of suggested clip Sum of logarithms with same base | Logarithms | Algebra II | Khan
0:00 0:51 Suggested clip Learn how to condense natural logs separated by subtraction YouTubeStart of suggested client of suggested clip Learn how to condense natural logs separated by subtraction
What are the logarithm properties? Product rule. Log b (M N) = log b (M) + log b (N) \\large\\log_b(MN)=\\log_b(M)+\\log_b(N) logo(MN)=logo(M)+logo(N) Quotient rule. Log b (M N) = log b (M) log b (N) \\large\\log_b\\left(\\franc{M}{N}\\right)=\\log_b(M)-\\log_b(N) logo(NM)=logo(M)logo(N)
This means that logarithms have similar properties to exponents. Some important properties of logarithms are given here. First, the following properties are easy to prove. For example, log51=0 l o g 5 1 = 0 since 50=1 5 0 = 1 and log55=1 l o g 5 5 = 1 since 51=5 5 1 = 5.
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