Logarithms

Rewrite log₂8 = 3 in exponential form

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2

Rewrite 3⁴ = 81 in logarithmic form.

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

Evaluate.
log₃81

• 4
• ¹/₄
• -4
• -¹/₄

State the property (s) used to simplify the expression

6log 2 = log 64

• Product Property

• Quotient Property

• Power Property

• Product and Power Property

Write the logarithm expression as a single logarithm

log₆25 - log₆5

• log₆125

• log₅20

• log₆5

• log₆30

Write the logarithm expression as a single logarithm

log₄60 - log₄4 + log₄x

• log₄15

• log₄15x

• log₄56x

• xlog₄30

 $f\left(x\right)=2\log_3\left(x+1\right)+5$ 
What is the range of the function?

•  $\left(-\infty,\infty\right)$  

•  $\left(5,\infty\right)$  

•  $\left(2,\infty\right)$  

•  $\left(1,\infty\right)$  

 $f\left(x\right)=2\log_3\left(x+1\right)+5$  
What is the domain of the function?

•  $\left(-\infty,\infty\right)$  

•  $\left(5,\infty\right)$  

•  $\left(1,\infty\right)$  

•  $\left(-1,\infty\right)$  

Solve for x
5^x = 17

• x = log₁₇5
• x = log 5 + log 17
• x = log₅17
• x = (log 5)/(log 17)

Logarithms and Exponentials are what?

• parallel
• perpendiular 
• inverses
• congurent