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Contract the expressions. that is, use the properties of logarithms

0 votes
to write each expression as a single logarithm with a coefficient of 1.?

A). ln 3-2 ln 7+ ln 14

B). ln 3-2 ln(7+8)

C). ln 3-2(ln 4+ ln 8)
asked Aug 11, 2014 in ALGEBRA 2 by anonymous

1 Answer

0 votes

(A).

The expressin is ln 3 - 2 ln 7 + ln 14.

Apply power property of logarithm : image.

ln 3 - 2 ln 7 + ln 14 = ln 3 - ln 72 + ln 14

= ln 3 - ln 49 + ln 14

Apply quotient property of logarithm : image.

= ln (3/49) + ln 14

Apply product property of logarithm : image.

= ln [ (3/49) * 14 ]

= ln [6/7].

Therefore, ln 3 - 2 ln 7 + ln 14 = ln [6/7].

(B).

The expressin is ln 3 - 2 ln (7 + 8).

Apply power property of logarithm : image.

ln 3 - 2 ln (7 + 8) = ln 3 - ln (7 + 8)2

= ln 3 - ln (15)2

Apply quotient property of logarithm : image.

= ln (3/152)

= ln [3/(15*15)]

= ln [1/75].

Therefore, ln 3 - 2 ln (7 + 8) = ln [1/75].

(C).

The expressin is ln 3 - 2(ln 4 + ln 8).

Apply product property of logarithm : image.

ln 3 - 2(ln 4 + ln 8) = ln 3 - 2ln (4*8)

= ln 3 - 2ln 32

Apply power property of logarithm : image.

= ln 3 - ln 322

Apply quotient property of logarithm : image.

= ln (3/322)

= ln [3/1024].

Therefore, ln 3 - 2(ln 4 + ln 8) = ln [3/1024].

answered Aug 11, 2014 by lilly Expert

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