Logarithm Laws Practice Worksheet
A Grade 10 math worksheet focusing on the application of logarithm laws for simplification and solving equations.
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Logarithm Laws Practice
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Date:
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Read each question carefully and apply the appropriate logarithm laws to simplify or solve. Show all your work.
1. Simplify the following expressions using the laws of logarithms:
a) log₃(9) + log₃(3)
b) log₂(32) - log₂(4)
c) 2 log₅(10) - log₅(4)
2. Complete the following logarithm laws:
a) logₐ(xy) =
b) logₐ(x/y) =
c) logₐ(xⁿ) =
3. Determine if the following statements are True or False:
a) log(x + y) = log(x) + log(y)
True
False
b) log(x²) = 2 log(x)
True
False
4. Which of the following is equivalent to log₄(x) - log₄(y)?
log₄(x - y)
log₄(x / y)
log₄(xy)
log₄(x + y)
5. Solve for x in the following equations:
a) log₂(x) + log₂(8) = 5
b) log₃(x) - log₃(2) = 2