EXPANDING AND CONDENSING LOGARITHMS
PROPERTIES OF LOGARITHMS Product Property: Quotient Property: Power Property: PROPERTIES OF LOGARITHMS
Product Property: PROPERTIES OF LOGARITHMS
= log a M + log a N EX. EXPRESS AS A SUM OF LOGARITHMS. 1) log a MN = log b A + log b T 2) log b AT = log M + log A + log T + log H 3) log MATH
= log 5 (193) EX. EXPRESS AS A SINGLE LOGARITHM 4) log log 5 3 5) log C + log A + log B + log I + log N = log CABIN
ON YOUR OWN Expanding the Logarithm (Write as a sum of logarithms):
ON YOUR OWN Expanding the Logarithm (Write as a sum of logarithms):
EX. EXPRESS AS A SUM OF LOGARITHMS, THEN SIMPLIFY. 6) log 2 (416) = log log 2 16 = 6 = 2 + 4
EX. 7 USE LOG 5 3 = AND LOG 5 7 = TO APPROXIMATE… log 5 (21) = log log 5 7 = = = log 5 (3 7)
PROPERTIES OF LOGARITHMS Quotient Property PROPERTIES OF LOGARITHMS
EX. EXPAND (EXPRESS AS A DIFFERENCE) 8) 9)
ON YOUR OWN Expanding the Logarithm (Write as a difference of logs):
ON YOUR OWN Expanding the Logarithm (Write as a difference of logs):
EX. 10 USE LOG 5 3 = AND LOG 5 7 = TO APPROXIMATE… = log 5 3 – log 5 7 = – =
PROPERTIES OF LOGARITHMS Power Property: PROPERTIES OF LOGARITHMS
= -5 log b 9 EX. EXPRESS AS A PRODUCT. 11) 12)
ON YOUR OWN Expanding the Logarithms:
ON YOUR OWN Expanding the Logarithms:
EX. 13 USE LOG 5 3 = AND LOG 5 7 = TO APPROXIMATE… = log = 2(1.209) = log 5 49 = 2 log 5 7
EX. 14 EXPAND = log5+ logy+ logx 3 = log5 + logy + 3 logx log5x 3 y
EX. 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 OWN Expanding the Logarithms:
ON YOUR OWN Expanding the Logarithms:
EX. CONDENSE. 16) 17)
Express all products as exponents Simplify the subtraction. Change the fractional exponent to a radical sign. Simplify the addition. EX 18 CONDENSE
PROPERTIES OF LOGARITHMS log a 1 = 0 log a a = 1 log a a x = x If log a x= log a ythen x = y because a 0 = 1 because a 1 = a Change-of-Base Product Property Quotient Property Power Property