Logarithmic Expansion Worksheet
Grade 10 Math worksheet covering logarithmic expansion properties and practice problems.
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Logarithmic Expansion Worksheet
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Expand each logarithmic expression completely using the properties of logarithms. Simplify your answers where possible.
1. The product rule for logarithms states that logb(MN) = .
2. The quotient rule for logarithms states that logb(M/N) = .
3. The power rule for logarithms states that logb(M^p) = .
4. Expand log(5x^3):
5. Expand ln( (a*b)/c ):
6. Expand log_2( (x^2 * y^5) / z ):
7. Which of the following is the correct expansion of log(x^2 * y)?
2log(x) + log(y)
log(x^2) * log(y)
log(x^2) + y
log(x) + 2log(y)
8. The expression log_b(x^2 / y^3) expands to:
2log_b(x) / 3log_b(y)
2log_b(x) - 3log_b(y)
log_b(2x) - log_b(3y)
log_b(x^2) + log_b(y^3)
9. The expansion of log(x/y) is log(x) - log(y).
True
False
10. log(x + y) can be expanded as log(x) + log(y).
True
False
11. Expand the following expression completely: log ( (x^2 * sqrt(y)) / (z^3 * w) )