EXPANDING AND CONDENSING LOGARITHMS PROPERTIES OF LOGARITHMS Product Property: Quotient Property:...

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Transcript of EXPANDING AND CONDENSING LOGARITHMS PROPERTIES OF LOGARITHMS Product Property: Quotient Property:...

Logarithms

Expanding and condensing logarithmsPROPERTIES OF LOGARITHMSProduct Property:

Quotient Property:

Power Property:PROPERTIES OF LOGARITHMS

PROPERTIES OF LOGARITHMSProduct Property:PROPERTIES OF LOGARITHMS

= loga M + loga NEx. Express as a sum of logarithms.1) loga MN = logb A + logb T2) logb AT = log M + log A + log T + log H3) log MATH

= log5 (193)Ex. Express as a single logarithm4) log5 19 + log5 35) log C + log A + log B + log I + log N= log CABINON YOUR OWNExpanding the Logarithm (Write as a sum of logarithms):

ON YOUR OWNExpanding the Logarithm (Write as a sum of logarithms):

Ex. Express as a sum of logarithms, then simplify.6) log2 (416)= log2 4 + log216= 6= 2 + 4

Ex. 7Use log53 = 0.683 and log57 = 1.209 to approximate log5 (21)= log5 3 + log5 7= 0.683 + 1.209= 1.892= log5 (37)PROPERTIES OF LOGARITHMSQuotient PropertyPROPERTIES OF LOGARITHMS

Ex. EXPAND (EXPRESS AS A DIFFERENCE)8)9)

ON YOUR OWNExpanding the Logarithm (Write as a difference of logs):

ON YOUR OWNExpanding the Logarithm (Write as a difference of logs):

Ex. 10 Use log53 = 0.683 and log57 = 1.209 to approximate = log5 3 log5 7= 0.683 1.209= -0.526PROPERTIES OF LOGARITHMSPower Property:

PROPERTIES OF LOGARITHMS

= -5 logb9Ex. Express as a product.

11)12)

ON YOUR OWNExpanding the Logarithms:

ON YOUR OWNExpanding the Logarithms:

Ex. 13 Use log53 = 0.683 and log57 = 1.209 to approximate = log5 72= 2(1.209)= 2.418log5 49= 2 log5 7Ex. 14 Expand = log5+ logy+ logx3= log5+ logy+ 3 logx log5x3yEx. 15 Expand

Simplify the division.

Simplify the multiplication of 4

Change the radical sign to an exponent

Express the exponent as a product

ON YOUR OWNExpanding the Logarithms:

ON YOUR OWNExpanding the Logarithms:

Ex. Condense.

16)17)

Express all products as exponentsSimplify the subtraction.Change the fractional exponent to a radical sign.

Simplify the addition.

Ex 18 Condense

Properties of Logarithmsloga1 = 0logaa = 1logaax = x

If loga x= loga ythen x = ybecause a0 = 1because a1 = a

Change-of-Base

Product PropertyQuotient PropertyPower Property

Warning!! Be careful!!