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Expand the following logarithms using one or more of the logarithm rules. Sometimes you need to write an expression as a single logarithm. Use the rules to work backwards. log3x2 + log3y . Use the Product Rule for Logarithms. Use the Power Rule for Logarithms. Simplify. Use the Quotient Rule for Logarithms. Simplify. Write as a single logarithm.
Example #1: Evaluate the expressions using a calculator. Properties of common logarithms (log) apply to natural logarithms (ln) as well. Log Rules and Properties (04:34) Example #2: Express 3 ln 5 as a single natural logarithm. Example #3: Express ln 35 – ln 5 as a single natural logarithm.
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PROPERTIES OF LOGARITHMS Definition: For 𝒚𝒚. x, b > 0, b. ≠. 1. 𝐥𝐥𝐥𝐥𝐥𝐥. 𝒃𝒃. 𝒙𝒙= 𝒚𝒚 𝒃𝒃= 𝒙𝒙. Natural Logarithm. 𝐥𝐥𝐥𝐥𝒙𝒙= 𝐥𝐥𝐥𝐥𝐥𝐥. 𝒆𝒆. 𝒙𝒙. Common Logarithm. 𝐥𝐥𝐥𝐥𝐥𝐥𝒙𝒙= 𝐥𝐥𝐥𝐥𝐥𝐥. 𝟏𝟏𝟏𝟏. 𝒙𝒙 ...
Worksheet by Kuta Software LLC Algebra 2 Properties of Logarithms Name_____ ©G o2P0v1b7O \KYuptLaE xSEoDfztswqaGrLeT \LNLBCy.g W TAdlil` ZrBiXgqhHtYs\ GrCehsMe[rAvgeldx. Condense each expression to a single logarithm. 1) 4log 9 10 - 6log 9 3 log 9 104 36 2) 12log 7 10 - 2log 7 11 log 7 1012 112 3) 4log 9 7 + 24log 9 10 log 9 (1024 × 74) 4) 5log 2
1. We often use logarithms for complicated calculatio ns involving large numbers, such as astronomical calculations, or scientific calculations. 2. John Napier discovered logarithms and the logarithm tables are called napier algorithms.
Properties of Logarithms Write the property of logarithms that each equation demonstrates. 3) log 6 9! = 6 log 6 9 4) log 5 5 + log 5 25 = log 5 125 5) log 7 2 – log 7 3 = log 7 6) Which property of logarithms does this equation demonstrate log 2 5" = 3 log 2 7) 5? a) Quotient Property b) Product Property c) Power Property 2 3 2 log 4 = log 4 ...