logs and exponentials

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27 Terms

1
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increasing exponential graph

f(x)=a^x
a>0, x>0
or
0<a<1, x<0

<p>f(x)=a^x<br>a&gt;0, x&gt;0 <br>or <br>0&lt;a&lt;1, x&lt;0</p>
2
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decreasing exponential graph

f(x)=a^x
a>1, x<0
or
0<a<1, x>0

<p>f(x)=a^x<br>a&gt;1, x&lt;0<br>or<br>0&lt;a&lt;1, x&gt;0</p>
3
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compound interest

A=final amount of money
p=principal started with
r=annual interest rate
n=number of times per year the interest compounds
t=number of years

<p>A=final amount of money<br>p=principal started with<br>r=annual interest rate<br>n=number of times per year the interest compounds<br>t=number of years</p>
4
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continuously compounded

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5
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change of base formula

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6
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natural base

e

7
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Product rule

log(MN)=logM +logN

8
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Quotient rule

log(M/N)=logM-logN

9
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Power rule

logM^p=plogM

10
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2⁷=x

Convert to exponential log₂x=7

11
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3⁵=x

Convert to exponential log₃x=5

12
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2

Evaluate log₃9

13
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6

Evaluate log₂64

14
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3.285

Evaluate log₄95

15
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2.355

Evaluate log₆68

16
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64

Evaluate log₈x=2

17
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15625

Evaluate log₅x=6

18
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log 4

condense & simplify log 2 + log 8 - log 4

19
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log 6/x

Condense & simplify log 3 + log 8 - log 4 - log x

20
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log 4 + 3log x

Expand log 4x³

21
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3(log 4 + log x)

Expand log (4x)³

22
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log 5 + log x - log 6 - log y

Expand log 5x/6y

23
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log 5 + log x - 6log y

Expand log 5x/y⁶

24
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log xy³/z²

Condense & simplify log x + 3log y - 2log z

25
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y= Log₂X

2∧y = x

26
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compounding "n" number of times

A= P(1+r/n)^nt

27
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compounding continuously

A=Pe^rt