Logarithm Properties Worksheets Grade 11

1. log₃(27) + log₃(9) - log₃(81) = ?
2. A right triangle is drawn on a coordinate plane with vertices at (0,0), (6,0), and (6,8). A circle is inscribed in this triangle, tangent to all three sides. What is the exact area of this inscribed circle?
3. Olivia is an environmental scientist studying the acidity of rainwater in two different regions. The pH of a solution is defined by the formula pH = -log[H⁺], where [H⁺] is the hydrogen ion concentration in moles per liter. In Region A, the hydrogen ion concentration is 5.0 × 10⁻⁵ M. In Region B, the hydrogen ion concentration is 2.0 × 10⁻⁶ M. Using properties of logarithms, determine how many times more acidic the rainwater in Region A is compared to Region B.

…and 5 more problems

1. Matiu is a volcanologist studying the energy released by two volcanic eruptions. He uses the Richter scale for volcanic events, where the magnitude M is given by M = log(E / E_0), with E being the energy released in joules and E_0 being a reference energy of 10^4 joules. The first eruption released 3.2 × 10^15 joules of energy. The second eruption released 6.4 × 10^14 joules of energy. Using the properties of logarithms, how many times more energy did the first eruption release compared to the second? Express your answer as a simplified integer or fraction.
2. A right triangle is drawn on a coordinate plane with vertices at (0,0), (8,0), and (8,6). A circle is circumscribed around this triangle, passing through all three vertices. What is the exact area of this circumscribed circle?
3. log₈(512) + log₉(729) - log₇(343) = ?

…and 4 more problems

1. log₃(81x) + log₃(x/9) = 6
2. log₂(32x) + log₂(x/2) = 7
3. log₄(64x) + log₄(x/16) = 4

…and 5 more problems