Logarithm review videos:

(old version of site)

Logarithm definition



Practice:
\( \ln e^x = e ^ {\ln 4} \)
What is x?

Click to show the answer



Log rule 1: Addition and multiplication


Practice:
Expand: \( \ln (x(x+4)(x-2)) \)

Click to show or hide the answer


Combine: \( \ln(2x+3) + \ln(x-5) \)

Click to show or hide the answer



Log rule 2: Subtraction and division



Practice:
Expand: \( \ln \left( \frac{(x+2)(x-2)}{x(x-4)} \right) \)

Click to show or hide the answer


Combine: \( \ln(2x+3) + \ln(x-3) - \ln(x+2) - \ln (x-10) \)

Click to show or hide the answer



Log rule 3: multiplication and powers.




Practice:
Expand: \( \ln \left( \frac{(x+2)^3(x-2)}{x^2(x-4)} \right) \)

Click to show or hide the answer


Combine: \( 2\ln(x) + \ln(x-3) - \ln(x+2) - 4\ln (x+1) \)

Click to show or hide the answer