Laws of logarithms - practice

Simplify: log(3) + 2log(5)

• log(75)
• 2log(15)
• log(30)
• log(13)

Simplify: log(16) - 3log(2)

• log(2)
• log(10)
• -3log(8)
• 3log(14)

Condense the following logarithm: 3 log₂ x + 2 log₂ y – 4 log₂ z 

• log₂ x³y²∕z⁴
• log₂ x³y²z⁴
• log₂ xyz⁹
• 9log₂ xyz

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand the following logarithm: 
log₂ 5x.

• log₂ 5 - log₂ x 
• log₂ 5 + log₂ x 
• 2log 5 + 2log x
• log5 2 + log_x 2

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand the following logarithm: 
log₂ 6/y 

• log₂ 6 - log₂ y 
• log₂ y - log₂ 6 
• 2log 6 + 2log y
• log₂ 6 - y

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Evaluate log_b(1)

• 0
• 1
• -1
• b

Evaluate log_b(b)

• -1
• 0
• 1
• b

Evaluate log_b(b^x)

• 1
• 0
• x
• b

Rewrite 3⁴ = 81 in logarithmic form.

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

Condense into a single log:

 $3\log2-\log4$  

Tags

CCSS.HSF.LE.A.4