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Logarithm and Exponential Forms 5 = log 2 (32) 2 5 = 32 Logarithm Form Exponential Form Base Stays the Base Logs Give you Exponents Input Becomes Output
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Logarithm Basics
The logarithm base a of b is the exponent you put on a to get b:
i.e. Logs give you exponents!
Definition of Logarithm
if and only lo
ifga
x
b x
a b
a > 0
and
b > 0
Logarithm and Exponential Forms
5 = log2(32)
25 = 32
Logarithm Form
Exponential Form
Base Stays the
BaseLogs Give you
Exponents
Input Becomes
Output
ExamplesWrite each equation in exponential form
1.log125(25) = 2/3
2.Log8(x) = 1/3
Write each equation in logarithmic form
1.If 64 = 43
2.If 1/27 = 3x
1252/3 = 25
81/3 = x
log4(64) = 3
Log3(1/27) = x
Original Inverse
Inverse of an Exponential Equation
Log’s give you exponents!
2xy 2yx
2logy xOR