Log

Solve log(x) + log(x+3) = 1

• 5

• -2

• -5

• 2

Answer explanation

Condense

log(x) + log(x+3) = 1

log(x^2 +3x) = 1

Rewrite in exponential form

10^1 = x^2 + 3x

0 = x^2 + 3x - 10

Factor and solve. Be sure to check!

Write the logarithm expression as a single logarithm

log₅4 + log₅3

• log₅7

• log₅12

• log₇5

• 3log₅4

Write the logarithm expression as a single logarithm

log₄60 - log₄4 + log₄x

• log₄15

• log₄15x

• log₄56x

• xlog₄30

Solve for x

• x = 3

• x = 5

• x = 1/4

• x = 1/3

• right 3

  reflected across x-axis

  up 2

  x=3

• left 3

  reflected across x-axis

  up 2

  x=-3

• right 3

  reflected across y-axis

  down 2

  x=3

• left 3

  reflected across y-axis

  down 2

  x=-3

• right 4

  reflected across y-axis

  down 2

  x=4

• left 4

  reflected across x-axis

  up 2

  x=-4

• right 4

  reflected across x-axis

  down 2

  x=-4

• left 4

  reflected across y-axis

  up 2

  x=4

• 10/41

• 13/12

• 41/10

• 12/13

x=3,

x=-4/25(ext)

x=4/25,

x=-3(ext)

x=25/3,

x=-4(ext)

x=4,

x=-25/3(ext)

• x=3,

  x=-4/25(ext)

• x=4/25,

  x=-3(ext)

• x=25/3,

  x=-4(ext)

• x=4,

  x=-25/3(ext)

• -1/2

• 1/2

• e^2

• e^-2

• (1/2) ln (k⁴y⁷) - (1/2) ln (p)³

• 2 ln k + (7/2) ln y - (3/2) ln p

• ln k⁴ + ln y⁷ +ln p³

• (1/2) ln k⁴ + 7 ln y - 3 ln p