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12 Cards in this Set
- Front
- Back
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The Natural Exponential Function
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The exponential function
f(x) = e^x with base e |
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Compound interest formula
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A(t) = P( 1 + r/n )^nt
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Continuously compounded interest
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A(t) = Pe^rt
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log(AB) = ?
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logA + logB
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log(A/B) = ?
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logA - logB
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log(A^C) = ?
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C*logA
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Expanding a logarithmic expression
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Using the Laws of Logarithms to write the logarithm of a product or a quotient as the sum or difference of logarithms
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Combining a logarithmic expression
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Using the Laws of Logarithms to write the sums and differences of logarithms as a single logarithm
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Guidelines for Solving Exponential Equations
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1) Isolate the exponential expression on one side of the equation.
2) Take the logarithm of each side, then use the Laws of Logarithm to "bring down the exponent." 3) Solve for the variable. |
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Exponential equation
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An equation in which the variable occurs in the exponent
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Logarithmic equation
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An equation in which a logarithm of the variable occurs
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Guidelines for Solving Logarithmic Equations
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1) Isolate the logarithmic term on one side of the equation; you may first need to combine the logarithmic terms.
2) Write the equation in exponential form. 3) Solve for the variable. |