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Day 4 Notes

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Solving exponential equations by taking the log of both sides.

Solving exponential equations by taking the log of both sides.

Published in: Education, Technology, Business

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  • 1. Base 10 and Other Base systems: • During the Exponents Unit we saw how to solve  exponential equations. For example: • To solve these types of problems we needed to  obtain a like base.   • Once the bases where like then I can set the  exponents equal to each other.   3x = 3 x = 1 • Today we are going to learn how to solve problems  where obtaining a like base is very difficult.  So we  need another way to solve those types of problems. 1
  • 2. Base 10 ­       Ex ­ Solve for x:   As you can see it would be very hard to rewrite this  equation with like bases.  Therefore the steps we will  use to solve this type of problem are: Step1 ­ Convert to logarithm. Step 2 ­ Solve by using graphing calculator Type in log253 =   2.4  Practice, Solve for x:          Step 1 ­ Convert to logarithm. Step 2 ­ Solve by using graphing calculator Type in log10000 =   4 2
  • 3. 3
  • 4. Not­Base 10 ­      Ex ­ Solve for x:  Using the steps from the previous problem:     1st ­ Convert to logarithm. 2nd ­ There's a problem.  Since the equation is not  base 10 system, you cannot use your calculator to solve  it. Our solution is to take the log of both sides of the  exponential equation. This converts the entire  equation to base 10 instead of base 3. original problem: step 1: log 3x = log 47 Step 2:  Now using the laws of logarithms rewrite the  equation: x log 3 = log 47 Step 3 :  Get x by itself: x = log 47  log 3 Step 4:  Now you can use your calculator to solve.   x = 3.5       4
  • 5. Now try this one:  9x = 14 5
  • 6.   2.  2x = 21 6
  • 7. x    3.  4 = 67 7
  • 8.   4.  102x = 3.5 8
  • 9.   5.  23x = 7 9