Logarithm Basics

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Logarithm Basics
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Definition of Logarithm
The logarithm base a of b is the exponent you put
on a to get b i.e. Logs give you exponents!
a gt 0 and b gt 0
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Logarithm and Exponential Forms
Logarithm Form
5 log2(32)
Base Stays the Base
Input Becomes Output
Logs Give you Exponents
25 32
Exponential Form
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Examples

• Write each equation in exponential form
• log125(25) 2/3
• Log8(x) 1/3
• Write each equation in logarithmic form
• If 64 43
• If 1/27 3x

1252/3 25
81/3 x
log4(64) 3
Log3(1/27) x
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Inverse of an Exponential Equation
Original Inverse

OR

• Logs give you exponents!