Logarithmic Form Solutions Worksheets Grade 11

1. Liam is analyzing the decay of a radioactive isotope used in medical imaging. The amount A(t) in milligrams after t years is given by A(t) = 200 × (1/2)^(t/12). How many years will it take for the isotope to decay to 25 milligrams? Express your answer in logarithmic form.
2. 14^x = 83. Express solution using logarithms.
3. A biologist is studying bacterial growth in a lab culture. The initial population is 500 bacteria, and it grows at a continuous rate of 8% per hour. The biologist needs to determine how many hours it will take for the population to reach 2,000 bacteria. Write your answer in logarithmic form.

…and 4 more problems

1. Matiu is studying the growth of a rare plant species in a controlled environment. The height H(t) of the plant in centimeters after t weeks is modeled by the exponential function H(t) = 12 × 3^(t/4). Matiu needs to determine after how many weeks the plant will reach a height of 108 centimeters. Express your answer in logarithmic form.
2. 7^(2x) = 32. Express solution using logarithms
3. A logarithmic spiral is drawn on a coordinate plane starting at point (2, 0). The spiral follows 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.

…and 4 more problems

1. 9^x = 47. Express solution using logarithms
2. The sound intensity level in decibels is given by the formula L = 10 log(I/I₀), where I is the sound intensity and I₀ is the reference intensity of 10⁻¹² W/m². If a rock concert measures 115 dB, how many times more intense is this sound than the threshold of hearing (0 dB)?
3. An archaeologist is analyzing the decay of carbon-14 in an ancient artifact. The artifact originally contained 120 micrograms of carbon-14, but now contains only 15 micrograms. Given that carbon-14 has a half-life of 5,730 years, determine how many years have passed since the artifact was created. Express your answer in logarithmic form.

…and 4 more problems