1001 Algebra Problems.PDF

Set 51 (Page 119)

801. b.Using the logarithm rules yields

3ln(xy^2 ) = – 4ln(x^2 y) + ln(xy) =

ln(xy^2 )^3 = – ln(x^2 y)^4 + ln(xy) =

ln+ ln(xy) =

ln =

ln =

ln

802. b.log 8 2 + log 8 4 = log 8 (2.4) = log 8 8 =1


803. c.4 log 9 3 = log 9 (3^4 ) = log 9 81 = 2


804. b.ln18x^3 – ln6x= ln(^168 xx
     ^3
     ) = ln3x^2


805. b.log 7  429 – log 7 ^27 = log 7 ( 429   72 ) = log 7 ( 429 ^27 )
     = log 7 ^17 = –1


806. d.3 log 4 ^23 + log 4 27 = log 4 (^23 )^3 + log 4 27 = log 4
      287 + log 4 27 = log 4 ( 287 27) = log 4 8 = ^32 


807. c.log (2x^3 ) = log 2 + logx^3 = log 2 + 3 logx


808. d.
     log 2 (^8 xy 2 z
     ^4
     ) = log 2 (8yz^4 ) – log 2 x^2 = log 2 8 + log 2
     y+ log 2 z^4 – log 2 x^2 = 3 + log 2 y+ 4log 2 z– 2log 2 x


809. d.
     ^32 log 2 4 – ^23 log 2 8 + log 2 2 =
     ^32 log 2 22 – ^23 log 2 23 + log 2 2 =
     ^32 (2) – ^23 (3) + 1 =
     3 – 2 + 1 =
     2


810. d.
     3 logb(x+ 3)–1– 2logbx+ logb(x+ 3)^3 =
     –3 logb(x+ 3) – 2logbx+ 3logb(x+ 3) =

- 2logbx=

logbx–2=

logb()

   811. c.

      ln (2x+ 1)(x^2 + 3)^4 =

ln (2x+ 1) + ln(x^2 + 3)^4 =

ln (2x+ 1) + 4ln(x^2 + 3) =

ln 2 + ln (x+ 1) + 4ln (x^2 + 3) =

ln 2 + ln (x+ 1) + 4ln (x^2 + 3) =

ln 2 + ^12 ln (x+ 1) + 4ln (x^2 + 3)

812. c.
     log 3

= log 3 (x^2  2 x– 1) – log 3 (2x+ 1)

= log 3 (x^2 ) + log 3 ( 2 x– 1) – log 3 (2x+ 1)

= log 3 (x^2 ) + log 3 (2x– 1) – log 3 (2x+ 1)

= 2log 3 (x) + ^12 log 3 (2x– 1) – ^32 log 3 (2x+ 1)

813. b.As the x-values decrease toward zero, the
     y-values on the graph off(x) = ln xplunge
     downward very sharply, as can be seen in the
     following graph:


814. b.The inputs for logarithmic functions must
     be positive. Since the input in this case is –x,
     then the inequality –x0 must be satisfied.
     Clearly –x0 =>x< 0. Thus the domain ofk
     is (–∞, 0).

1 2 3 x

–3–2–1 4 5 6 7 8 910

–2

–4

4

2

1

–1

–3

–5

3

^12 ^32

^32

^32

x^2 ^2 x– 1

(2x+ 1)^32 

^12

^1

x^2

y^3

x^4

x^3 y^6 xy

x^8 y^4

(xy^2 )^3 (xy)

(x^2 y)^4

(xy^2 )^3

(x^2 y)^4

ANSWERS & EXPLANATIONS–