q uestions How many times do I need to multiply 1 by 2 to get 64 Try this on your calculator and write an equation that gives the answer We will compare answers afterwards How many times do I need to multiply 1 by 2 to get 128 ID: 131139
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Slide1
The answer to exponential
q
uestionsSlide2
How many times do I need to multiply 1 by 2 to get 64?
Try this on your calculator and write an equation that gives the answer.
We will compare answers afterwards.Slide3
How many times do I need to multiply 1 by 2 to get 128
Try this on your calculator and write an equation that gives the answer.
We will compare answers afterwards.Slide4
How many times do I need to multiply 1 by 2 to get one million
Try this on your calculator and write an equation that gives the answer.
We will compare answers afterwards.Slide5
The answer to these exponent questions is called has a special name called a
logarithm
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The small number after log is called the “base”. This is what number you are raising to a power.
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Note that powers and logarithms are inverse operations
This means to undo taking a power, you take a logarithm:
=b and
.
This is reasonable: “What power do I need to raise a to in order to get
?” is simply b.
“Raising a to the whatever power would give b, does give b”
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How do you feel up to this point?
I feel like I understand things
I am a little confused
I am very confused
Not sureSlide12
How many times do I need to multiply 1 by 2 to get 8 x 8?
You could do this two ways.
First, multiplying by 2 three times is the same as multiplying 8. So you can multiply by 2 three times, then multiply by 2 three more times. This means it takes 3+3 times.
Or, you could simply compute 8x8=64, and then find it takes 6 times to get 64.Slide13
This is because
=
This method holds true in general. We can use the power rules we already know and the fact that powers and logarithms are inverse operations in order to prove this.Slide14
Proof that
=
(Using everything that has been mentioned so far)
=ab
T
ake the logarithm the left and right side.
=
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Proof that
(Using everything that has been mentioned so far)
.
T
ake the logarithm the left and right side.
(This works for any base)
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How do you feel up to this point?
I feel like I understand things
I am a little confused
I am very confused
Not sure