07.04 Notes.docx

# States that a coefficient on a logarithmic term can

• Notes
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states that a coefficient on a logarithmic term can be moved to the exponent of its argument and an exponent can become a coefficient. Therefore, the exponent of x becomes the coefficient on the logarithmic expression log 2. x log 2 = log 8 While it may seem excessive to include so many decimal positions, it will affect the solution if you round after only two or three places. So, try not to round until the very end. Notice that the base of each logarithm is 10. That's good news! You can use your calculator to find the value of log 2 and log 8. Remember, some calculators require the log be input first while others need the argument first. x (0.3010299957) ≈ 0.903089987 0.3010299957x/0.3010299957=0.903089987/0.3010299957 0.3010299957x ≈ 0.903089987 x ≈ 3 This process becomes very useful when solving equations where one side of the equation cannot match the base of the other side such as 4 x = 7 x + 1 .

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A Deeper Look With exponential equations like A = P (1 + r) t, there are a number of parts that can affect the entire equation. Understanding how each part works in the equation will help when you need to create an exponential equation to model a real-world situation. A Plain and simple, the A represents the amount after the exponential growth or decay has occurred. Exponential equations are great if you are looking to solve
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