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Thursday, June 28, 2012. Properties of Logarithms. Review Homework. IRespond Homework Quiz. Basic Properties of Logarithms. Product Property. Express as a sum of logarithms (e x p a n d). 1) log a MR. = log a M + log a R. 2) log b CH. = log b C + log b H. 3) log MATH.
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Thursday, June 28, 2012 Properties of Logarithms
Product Property Express as a sum of logarithms (e x p a n d). 1) loga MR = loga M + loga R 2) logb CH = logb C + logb H 3) log MATH = log M + log A + log T + log H
Express as a single logarithm (condense). 4) log5 19 + log5 3 = log5 (19*3) 5) log C + log A + log B + log I + log N = log CABIN
Ex. Express as a sum of logarithms, then simplify 6) log2 (4*16) = log2 4 + log216 = 2 + 4 = 6
Ex. 7 Use log53 = 0.683 and log57 = 1.209 to approximate… log5 (21) = log5 (3*7) = log5 3 + log5 7 = 0.683 + 1.209 = 1.892
1) Ex. Expand the expression 2)
Ex. 3 Use log53 = 0.683 and log57 = 1.209 to approximate… = log5 3 - log5 7 = 0.683 - 1.209 = -0.526
Ex. Express as a product (expand). = -5 * logb9 1) 2)
Ex. 6 Use log53 = 0.683 and log57 = 1.209 to approximate… log5 49 = log5 72 = 2 log5 7 = 2(1.209) = 2.418
Ex. 1 Expand. log105x3y log105 + log10x3 + log10y log105 + 3 log10x + log10y
Ex. 2 Expand • Simplify the division. • Simplify the multiplication • Change the radical sign to an exponent • Express the exponent as a product
Ex. Condense. 3) 4)
Ex 5 Condense • Express all products as exponents • Change the fractional exponent to a radical sign. • Simplify the subtraction. • Simplify the addition.
Properties of Logarithms loga1 = 0 because a0 = 1 logaa = 1 because a1 = a logaax = x If loga x= loga y then x =y Product Property Quotient Property Power Property Change-of-Base
