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Exponentials without Same Base and Change Base Rule

Exponentials without Same Base and Change Base Rule. Objectives. I can solve an exponential equation that does not have the same base I can use the Change Base Rule to evaluate log expressions. Common Logarithms. Your calculator has a button in the 7 th row called LOG.

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Exponentials without Same Base and Change Base Rule

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  1. Exponentials without Same BaseandChange Base Rule

  2. Objectives • I can solve an exponential equation that does not have the same base • I can use the Change Base Rule to evaluate log expressions

  3. Common Logarithms • Your calculator has a button in the 7th row called LOG. • This button will calculate the base 10 common logarithm of a number. • Example: log 125 • = 2.097 • ROUND to 3 decimal places

  4. Example • log 135 • = 2.130

  5. Using Logarithms to Solve Exponents • So far we have solved exponents using the principle of getting the same base, then setting the exponents equal. • There are many times that we cannot get the same base, so we need to solve a different method.

  6. Solve for x 2(x+1) = 8 2(x+1) = 23 x+1 = 3 x =2 Solve for x 8(2x-5) = 5(x+1) If this problem we cannot get the same base To work this new type problem, we will use logarithms Old Problems vs New

  7. Rule for Logarithms • Logarithms can be applied to equations. • In any equation, if I do something to one side, I must do the same thing to the other side to keep equality. • In these problems, we will take the Common Log of both sides of each equation, then use the Power Property

  8. Log Power Property

  9. Example

  10. Using the Property • We will use this property when solving exponential equations that do not have the same base

  11. Solve for x • 8(2x-5) = 5(x+1) • log 8(2x-5) = log 5(x+1) • (2x-5) log 8 = (x+1) log 5 • (2x–5) (.9031) = (x+1) (.6990) • 1.81x – 4.52 = .699x + .699 • 1.11x = 5.22 • x = 4.70

  12. Change of Base Formula

  13. Find: log8 77

  14. Find: log16 64

  15. Homework • WS 12-5

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