Logarithmic Form Solutions Worksheets Grade 11

1. A logarithmic spiral is graphed on a coordinate plane with the polar equation r(θ) = 3e^(0.2θ). The spiral intersects a ray from the origin that makes a 60° angle with the positive x-axis. Find the exact distance from the origin to this intersection point, expressing your answer in logarithmic form.
2. A research scientist is studying bacterial growth in a lab culture. The population P(t) after t hours is modeled by the equation P(t) = 5000 * e^(0.15t). After how many hours will the bacterial population reach 25,000? Express your answer in logarithmic form.
3. A radioactive substance decays according to the model A(t) = 800e^(-0.045t), where A is the amount in grams and t is time in years. After how many years will only 200 grams remain? Round your answer to the nearest tenth of a year.

…and 5 more problems

1. Lena is studying sound intensity levels in her physics class. She learns that the decibel level of a sound is given by the formula dB = 10 × log(I/I₀), where I is the sound intensity and I₀ is the reference intensity of 10⁻¹² W/m². If Lena measures a sound at 85 decibels, what is the ratio of its intensity to the reference intensity? Express your answer in logarithmic form.
2. 7^(x+2) = 49. Express solution using logarithms
3. 5^(3x-1) = 125. Express solution using logarithms.

…and 5 more problems

1. A financial analyst is modeling compound interest for an investment account. The account balance A(t) after t years is given by A(t) = 2500 × (1.045)^t. If the investor wants to know when the account will reach $5,000, express the time t in logarithmic form.
2. 11^x = 37. Express solution using logarithms
3. A right triangle is drawn on a coordinate plane with vertices at (0,0), (4,0), and (4,3). A circle is inscribed within this triangle such that it is tangent to all three sides. What is the radius of this inscribed circle?

…and 5 more problems