University:
University of Central Arkansas
Course:
MATH 1486 | Calculus Preparation
Academic year:

2024
Views:

372

Pages:

14
Author:

Tristan Miller

Pre-Calculus 12 Unit 4 Send-In Assignment On-Line Course All answers rounded to 2 decimal places unless otherwise stated. Change the following to exponential form: log_m a = p a = m^p Change the following to logarithmic form: e^d = e log_e e = d Evaluate: log_5 70 log_5 70 = log 70 / log 5 ≈ 2.64 Solve the following for x: a) 9^(x+1) = 81^(x-4) x = 9 b) 125^(x+2) = (1/5)^(1-5x) x = 7/2 **Pre-Calculus 12** **Unit 4 Send-In Assignment** **On-Line Course** **13. An earthquake off the coast of Vancouver Island was measured at 8.9 on the Richter Scale and an earthquake off the coast of Alaska was measured at 6.5. How many times more intense, to the nearest whole number, was the earthquake off the coast of Vancouver Island than the one off the coast of Alaska?** 10^(8.9-6.5) = 10^2.4 ≈ 251 times as strong **14. A major earthquake of magnitude 8.3 is 120 times as intense as a minor earthquake. Determine the magnitude, to the nearest tenth, of the minor earthquake.** Let x be the magnitude of the minor earthquake. Then 10^8.3 = 120 * 10^x 10^(8.3-x) = 120 (8.3-x)log10 = log120 (8.3-x)(1) = log120 x = 8.3 - log120 x ≈ 6.12 **15. Determine the inverse function of f(x) = 3^(x-1) - 2.** x = 3^(y-1) - 2 x + 2 = 3^(y-1) log(x+2) = (y-1)log3 log(x+2)/log3 = y-1 y = log₃(x+2) + 1 f^(-1)(x) = log₃(x+2) + 1 **Image Description:** The image is a handwritten page or pages from a pre-calculus assignment. It focuses on logarithmic and exponential functions. The assignment includes three questions: 1. **Comparing Earthquake Intensities:** This question involves using the Richter scale to compare the intensity of two earthquakes. 2. **Determining Earthquake Magnitude:** This question requires solving an exponential equation to find the magnitude of a smaller earthquake given its intensity relative to a larger one. 3. **Finding the Inverse Function:** This question involves finding the inverse of a given exponential function using algebraic manipulation. The handwriting is clear and easy to read, making the content accessible. The page is well-organized with numbered questions and clear calculations. Overall, the image provides a glimpse into a pre-calculus assignment

Exponents and Logarithms Unit Review

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