Product rule of logarithms

Product rule of logarithms

Lessons

logb(XY)=logbX+logbY \log_b(X \cdot Y) = \log_b X + \log_b Y
  • 1.
    How and when to use the product rule:
    Without using a calculator, evaluate: log2(1632) {\log_2(16 \cdot 32)}

  • 2.
    log33+log327{\log_3 \sqrt{3} + \log_3 \sqrt{27}}

  • 3.
    Express as a single logarithm:
    a)
    log26+log25\log_2 6 + \log_2 5

    b)
    log3100+log65 \log_3 100 + \log_6 5\