7.3
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Transcript of 7.3
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7.3 LOGARITHMIC FUNCTIONS AS INVERSES
Part 1: Introduction to Logarithms
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Logarithms
The inverse of the exponential function is the logarithmic function. By definition, y = bx is equivalent to logby =
x. Logarithms exist only for positive real numbers.
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Logarithms
The definition of a logarithm can be used to write exponential functions in logarithmic form: y = bx is equivalent to logby = x
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Example:
Write each equation in logarithmic form100 = 102
y = bx is equivalent to logby = x
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Example:
Write each equation in logarithmic form81 = 34
y = bx is equivalent to logby = x
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Logarithms
To write a logarithmic function in exponential form, use the definition:
If y = bx is equivalent to logby = x,
then logby = x is equivalent to y = bx
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Example
Write each equation in exponential form.log2128 = 7
logby = x is equivalent to y = bx
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Example
Write each equation in exponential form.log716,807 = 5
logby = x is equivalent to y = bx
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Logarithms
The exponential form of a logarithm can be used to evaluate a logarithm.1. Write a logarithmic equation (set the
log = x)2. Use the definition to write the
logarithm in exponential form3. Write each side of the equation using
the same base4. Set the exponents equal to each
other5. Solve
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Example:
Evaluate each logarithmlog5125
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Example:
Evaluate each logarithmlog832
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Example:
Evaluate each logarithm
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Common Logarithm
The common logarithm is a logarithm with base 10log10
The common logarithm can be written without a base, because it is understood to be 10log10x = log x The “log” key on your calculator is the common
logarithm
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Homework
P456 #12 – 35