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Natural Base Expressions
Exponetial expressions
Simplifying logs and exponentials
Properties of logarithms
Change Base Formula
100
e
What is the natural base
100
log3(9)=2
3^2=9
100
lne^-2x
-2x
100
Use the Quotient property for this equation to simplify Log3(6/5)
Log3(6)-Log3(5)
100
What is the formula used for change of base?
Big Log/ Small Log
200
e^8 x e^2
e^10
200
2^-3 write as a logarithm
log2(1/8)=-3
200
e^ln4.5
4.5
200
Use the power property to simplify this equation- Log3(6^2)
2Log3(6)
200
Use change of base to solve Log2(12)
3.585
300
18e^10 / 3e^5
6e^5
300
5^0=___
1
300
10^log3x
3x
300
What is the equation for the power property?
logb(m^n)=nlogb(m)
300
Use change of base formula to solve- Log4(16)
2
400
2(e^3)^2
4e^6
400
log10=___
1
400
log4(4)^7x
7x
400
What is the equation for the quotient property?
logb(m/n)=logb(m)-logb(n)
400
log2(6)
2.584
500
The formula for compund intrest
A=Pe^rt
500
log2(16)=4 write in exponential form
2^4=16
500
Give the definition of a common logarithm
A logarithm with a base of 10, denoted by log
500
What is the equation for product property?
logb(mn)=logb(m) + logb(n)
500
Use change of base to solve- Log99(123456)
2.55