Logarithmic Properties
This worksheet focuses on applying and understanding the fundamental properties of logarithms at a Grade 12 level.
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Logarithmic Properties
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Read each question carefully and apply the appropriate logarithmic properties to solve. Simplify your answers where possible.
1. The product rule states that logb(MN) = .
2. The quotient rule states that logb(M/N) = .
3. The power rule states that logb(Mp) = .
4. The change of base formula allows us to write logb(M) as .
1. Expand the expression: log(5x^3y^2)
2. Expand the expression: ln(sqrt(x)/z^4)
1. Condense the expression: 3logx + 2logy - logz
2. Condense the expression: (1/2)ln(a) - 4ln(b)
1. Which of the following is equivalent to logb(x) + logb(y) - logb(z)?
logb(xy/z)
logb(x+y-z)
logb(x)logb(y)/logb(z)
logb(xyz)
2. If log3(x) = 2, what is the value of x?
6
9
8
5
1. logb(1) = 0 is always true for any valid base b.
True
False
2. ln(e^x) = x is true for all real numbers x.
True
False