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Session 9 In-Class Exercise Solutions

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Q 1. Solve for x. 5 "#$ % = 52. Solve for x. Round your answer to 2 decimal places. 32x + 3x – 30 = 0 3. Solve for x: ln (x – 3) – ln (x + 3) = ln / '4. Solve for x: log4(x – 2) + log4(x + 1) = 15. The exponential equation A = 108.3e0.012t describes the population of a particular country in millions t years after 2003. When will the population of the country be 150 million?

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1.5 "#$ % = 5 % 5 "#$ % = 5 $ % '() * = ) * x – 1 = 1 x = 2 2.32x + 3x – 30 = 0 Applying Power Rule for (3x)2 + 3x – 30 = 0 Exponents: 32x = (3x)2 u2 + u – 30 = 0 Let u = 3x (u – 6) (u + 5) = 0 u + 6 = 0 Factor and find the values of u u = -6 u – 5 = 0 u = 5 3.u = -6 u = 5 3x = -6 x = log3 -6 Not a solution. Domain: all positive real numbers 3x = 5 x = log3 5 x = +,- . +,- * = 1.46