Logarithm review videos: New and improved!
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Logarithm definition
Practice:
\( \ln e^x = e ^ {\ln 4} \)
What is x?
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Log rule 1: Addition and multiplication
Practice:
Expand: \( \ln (x(x+4)(x-2)) \)
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\( \ln(x)+\ln(x+4)+ln(x-2) \)
Combine: \( \ln(2x+3) + \ln(x-5) \)
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Log rule 2: Subtraction and division
Practice:
Expand: \( \ln \left( \frac{(x+2)(x-2)}{x(x-4)} \right) \)
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\( \ln(x+2)+\ln(x-2)-\ln(x)-\ln(x-4) \)
Combine: \( \ln(2x+3) + \ln(x-3) - \ln(x+2) - \ln (x-10) \)
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\( \ln \left( \frac{(2x+3)(x-3)}{(x+2)(x-10)} \right) \)
Log rule 3: multiplication and powers.
Practice:
Expand: \( \ln \left( \frac{(x+2)^3(x-2)}{x^2(x-4)} \right) \)
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\( 3\ln(x+2)+\ln(x-2)-2\ln(x)-ln(x-4) \)
Combine: \( 2\ln(x) + \ln(x-3) - \ln(x+2) - 4\ln (x+1) \)
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\( \ln \left( \frac{x^2(x-3)}{(x+2)(x+1)^4} \right) \)