Logarithmic Laws

log (a²b) = ?

• 2log(a) + log(b)

• 2log(a) + 2log(b)

• log(a) + log(b)

• 2log(a) x log(b)

Write as a single logarithm:

log16 + log2 - log8

• log4

• log8

• log10

• log24

Write log₃ 81 = 4 in exponential form.

• 81⁴=3
• 81³=4
• 4³=81
• 3⁴=81

Tags

CCSS.HSF.BF.B.5

Write log₆ 216 = 3 in exponential form.

• 3⁶=216
• 6³=216
• 216⁶=3
• 3²¹⁶=6

Tags

CCSS.HSF.BF.B.5

Find the domain and range of:
f(x) = log₂(x)

• D: all real numbers
  R: y > 0
• Domain: all real numbers
  Range: all real numbers
• Domain: x > 0
  Range: all real numbers
• Domain: all real numbers
  Range: y < 0

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.5

Evaluate: log₆₄4 = x

• x = 3

• x = -3

• x = ⅓

• x = -⅓

Tags

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Which expression is equivalent to  $\log_{ }4n^3$  ?

•  $3\left(\log4\ +\log n\right)$  

•  $3\cdot\log4\ +\log n$  

•  $\log4+3\log n$  

•  $\log64+3\log n$  

Which expression is equivalent to  $\frac{5}{2}\log_4x\ -3\log_4y$  

•  $\log_45x^2-3y$  

•  $\log_4\ \frac{5x^2}{y^3}$  

•  $\log_45x^2y^3$  

•  $\log_4\ \frac{x^2\sqrt{x}}{y^3}$  

Evaluate  $\log_mm^{2n}$  .

•  $n$  

•  $n^2$  

•  $mn$  

•  $2n$  

Write as a single logarithm:  $\log_6\left(x-3\right)+\log_6x$  

•  $\log_6\left(x^2-3x\right)$  

•  $\log_6\left(2x-3\right)$  

•  $\log_{12}\left(x^2-3x\right)$  

•  $\log_6\left(-x\right)$