Lesson 32 Practice

  1. Change to Natural Logarithms.

    a) \frac{ln 12}{ln 3} = 2.262

    b) \frac{ln 17}{ln 7} = 1.456

  2. Change to Base-10.

    a) \frac{log _{10}200}{log _{10}3} = 4.823

    b) \frac{log _{10}4/25}{log _{10}7} = -0.942

  3. Evaluating Logarithmic Expressions. a) 3.907 b) -0.208 c) -0.558 d) 1.077
  4. Expanding Logarithmic Expressions I. a) \log _63+\log _6n b) \ln x-\ln 4 c) 3\log _8x+3\log _8y
  5. Natural Logs of 3 and 5. a) \ln 3+\ln 5 b) \ln 3-\ln 5 c) 2\ln 5+\ln 3
  6. Challenge: Expanding Logarithmic Expressions II. a) 1+\log _2y+\frac{1}{2}\log _2(y-3) b) 2\ln x+\ln y-\ln 4
  7. Condensing Logarithmic Expressions I. a) \log _4(\frac{x}{5}) b) \log _{10}yx^2 c) \ln (\sqrt{3x}\cdot (2x+1))
  8. Challenge: Condensing Logarithmic Expressions II. a) \log _2(\frac{((x+2)^3\cdot (x-1)^4)}{x^3}) b) \ln (\frac{y^5}{2x(x+1)})
  9. No More Fractions. a) -\log _514 b) -\log _2400