Logarithms and Their Properties

Evaluate:
log₄16

• 2
• 4
• 1/2
• -2

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Tags

CCSS.HSF.BF.B.5

Write in logarithmic form.
2^-4 = ¹/₁₆

• log₂(¹/₁₆) = -4
• log_-4(¹/₁₆) = 2
• log _-4 2 = ¹/₁₆
• log₂(-4) = ¹/₁₆

Tags

CCSS.HSF.BF.B.5

Write in exponential form.
log₂(¹/₈) = -3

• 2^-3 = ¹/₈
• 2^1/8 = -3
• -3² = ¹/₈
• -3^1/8 = 2

Tags

CCSS.HSF.BF.B.5

Evaluate.
log₆(¹/₂₁₆)

• 3
• ¹/₃
• -¹/₃
• -3

Evaluate.

log₂₇81

• 4⁄3

• 3⁄4

• 3

• -3

Rewrite log_pt = m in exponential form.

• p^t = m
• t^m = p
• m^t = p
• p^m = t

Tags

CCSS.HSF.BF.B.5

Simplify:  $\log_73+\log_76$  

•  $\log_79$  

•  $\log_7\left(\frac{1}{2}\right)$  

•  $\log_718$  

•  $\log_7729$  

Simplify:  $\log_4\left(x+4\right)-\log_4\left(x-5\right)$  

•  $\log_49$  

•  $\log_4\left(2x-1\right)$  

•  $\log_4\left(x^2-x-20\right)$  

•  $\log_4\left(\frac{x+4}{x-5}\right)$  

Simplify:  $2\log_3\left(11x\right)$  

•  $\log_3\left(22x\right)$  

•  $\log_3\left(121x\right)$  

•  $\log_3\left(121x^2\right)$  

•  $\log_3\left(11x^2\right)$