Laws of Logarithms

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)

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

• log₂ x³y²∕z⁴

• log₂ x³y²z⁴

• log₂ xyz⁹

• 9log₂ xyz

Rewrite 3⁴ = 81 in logarithmic form.

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

Tags

CCSS.HSF.BF.B.5

Use the change of base rule to rewrite this problem:

log₅75

• log(75)/log(5)

• log(5)/log(75)

Use the change of base rule to rewrite this problem:

log₃64

• log(64)/log(3)

• log(3)/log(64)

Solve.

• 0.2560

• 0.4926

• 3.9069

• 7.5

Tags

CCSS.HSF.LE.A.4

Change $\log_5⁡7$ into the form of $\frac{\log_3⁡a}{\log_3⁡b}$ ,  where  $a$ and $b$ are integers

•  $\frac{\log_3⁡5}{\log_3⁡7}$  

•  $\frac{\log_3⁡7}{\log_3⁡5}$  

If  $\log_3⁡2=a$ , express $\log_4⁡18$  in terms of $a$  .

•  $\frac{2a}{a+2}$  

•  $\frac{a+2}{2a}$  

•  $\frac{9}{2a}$  

•  $\frac{9a}{6}$  

If  $\log_3⁡2=a$ , express $\log_2⁡12$  in terms of $a$  .

•  $\frac{2a+1}{a}$  

•  $\frac{a}{2a+1}$  

•  $6a$  

•  $\frac{2+a}{a}$