Solving Exponential and Logarithmic Equations Exponential Equations (variable in exponent position) 1. Isolate the exponential portion ( base exp onent ): Move all non-exponential factors or terms to the other side of the equation. 2. Take ln or log of each side of the equation. • Make sure to use ln if the base is “e”. Then remember that ln e = 1 . • Make sure to use log if the base is 10. • If the base is neither “e” nor “10”‚ use either ln or log‚ your choice.. 3. Bring the power (exponent)
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of Equations Part 1 1. Tony and Belinda have a combined age of 56. Belinda is 8 more than twice Tony’s age. How old is each? Tony’s age = t years‚ Belinda’s age = 56 - t years 56 - t = 2t + 8 56 - 8 = 2t + t ==> 3t = 48 ==> t = 16 years THUS Tony = 16 years‚ and Belinda = 40 years 2. Salisbury High School decided to take their students on a field trip to a theme park. A total of 150 people went on the trip. Adults pay $45.00 for a ticket and students pay $28.50 for a ticket. How many
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The Form of Structural Equation Models Structural equation modeling incorporates several different approaches or frameworks to representing these models. In one well-known framework (popularized by Karl Jöreskog‚ University of Uppsala)‚ the general structural equation model can be represented by three matrix equations: However‚ in applied work‚ structural equation models are most often represented graphically. Here is a graphical example of a structural equation model: For more information
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problem‚ is 60 degrees‚ and that the period is 24 hours. Since Period = 2p/B‚ B = 2p/24. The problem stated that the axis of the sinusoid is shifted to - 5 degrees‚ so D or the vertical shift equals - 5 degrees. To find the horizontal shift‚ we used the formula Starting Point = C/B. As given in the problem statement‚ the maximum angle of elevation occurs at 12:45 p.m. We took the time 12:45 p.m. where the maximum angle of elevation occurred and changed it to 12.75 because 45/60 is equal to
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The Drake Equation is used to estimate the number of civilizations in the universe. It is more of a tool to use and help us understand and figure out how many worlds are out there. Each of the terms are being multiply to get the outcome for N‚ which is the number of civilizations in The Milky Way Galaxy whose electromagnetice missions are detectable. According to SETI website‚ the Drake Equation values R*‚fp‚ ne‚ fl‚ fi‚ fc‚ L are defined as the following. In the first part of the equation is R*.
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Have you ever wanted your own business? What type of business partner are you looking for? According to Eric Basu there are 6 questions that should be asked before picking a business partner. First‚ one should ask whether he or she needs a business partner. Second‚ the goals of the prospective partner and the owner should either be the same or coincide with one another. Next is the designation of tasks followed by how the conflicts will be resolved. The last two focus on the future of the business
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Communication: An Equation The transactional model of communication is an infinitely long‚ incredibly complex ‘web’ of perceptions‚ actions‚ predictions‚ and reactions that perpetuate/transfer among people. The transactional model of communication can be compared to a simple but extensive equation. To avoid the subjectivity about numbers and their representation of quantities and physical properties in math‚ I’ll be using (#) to represent people. Ex. # + # Represents two people in communication
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Calculate the molecular mass/formula weight for: KHSO3 2. How many of each type of atom are present in 0.667 mol of [CrCl2(NH3)4]Cl 3. Calculate the molecular formula for the compound that contains 40.92% C‚ 4.58% H‚ 54.50% O‚ and has a molecular mass of 176 u. 4. When 1.019 g of potassium reacts with O2‚ it forms 1.860 g of a rather strange compound. Find the empirical formula of this compound‚ and explain why it is strange. 5. How many grams of BaSO4 (s) are formed when an excess of BaCl2
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Backward Bending Slutsky Equation In the Labor Supply Model‚ consumer has a choice between consumption and leisure. If they were to reduce their leisure and allocate more time working‚ they will be able to consume more. The amount of labor and consumption are determined by the interaction of consumer’s preferences and budget constraint. In this model‚ the utility function to be maximized is U(C‚L)‚ where individual cares about consumption (C) and leisure (L). The utility function is subjected
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❶AGE PROBLEM In three more years‚ Miguel’s grandfather will be six times as old as Miguel was last year. When Miguel’s present age is added to his grandfather’s present age‚ the total is68. How old is each one now? This exercise refers not only to their present ages‚ but also to both their ages last year and their ages in three years‚ so labelling will be very important. I will label Miguel’s present age as "m" and his grandfather’s present age as "g". Then m + g = 68. Miguel’s age "last year"
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