Evaluating Logarithms

Evaluating Logarithms

Agenda

• Relay race competition.

• Quiz corrections.

• Quick notes on evaluating logarithms.

• Launch Lost Project. (in-person only).

Success Criteria.

• You will be able to evaluate easy logarithms like

   $\log_525$  with no calculator.

• You will be able to evaluate hard logarithms like  $\ln57$  with a calculator.

• You will be able to apply logarithm knowledge to our project.

Recall

• Logarithms answer the question, "How many of one number do we multiply to get another number."

• For example: How many 3's do we multiply to get 27? (or  $3^x=27$  )

• Logarithms are the inverses of exponents.

• With a partner: create arrows showing the connections between  $3^5=243\ and\ \log_3\ 243\ =5$  

Multiple Choice

Change to Logarithmic Form:
12² = 144

• log ₂ 144 = 12
• log ₁₂ 144 = 2
• log ₁₂ 2 = 144
• log ₂ 12 = 144

Multiple Choice

Rewrite log₂8 = 3 in exponential form.

• 2⁸ = 3
• 2³ = 8
• 3² = 8
• 8³ = 2

Multiple Choice

Rewrite the exponential equation into its logarithmic equation; x⁶=64

• log₆x=64

• log6=64

• log₆64=x

• log_x64=6

Evaluating Easy Logarithms (like

 $\log_327$  )

• Be thinking: "How many times do I multiply 3 by itself to get 27?"

• It might help to rewrite it in exponential form like  $3^x=27$  .

Multiple Choice

log ₂ 16

• 3

• 2

• 4

• 5

Multiple Choice

log 1000 =

• 1/10

• 10

• 1/3

• 3

Multiple Choice

log ₃ 9 =

• 1/2

• 2

• 1/3

• 3

A Kool pattern extension.

•  $\log_28\ vs.\ \log_82\ \ vs.\ \log_2\ \frac{1}{8}\ vs.\ \ \log_8\ \frac{1}{2}$  

• You try:  $\log_416\ vs.\ \log_{16}4\ vs.\ \log_4\ \frac{1}{16}\ vs.\ \log_{16}\ \frac{1}{4}$  

Evaluating harder logarithms.

• Some logarithms may be difficult to solve by hand. For now, we can use a calculator to help us solve larger application problems! (we are going to be learning a trick soon so we can ditch the calculators ;-) )

• For example,   $\log_346$  cannot be done easily by hand. Throw it in the calculator! (Symbolab is a great online calculator..)