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01-Jun-2015
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Rewriting exponential form to logarithm form and back. Solve logarithm equations.

### Transcript of Common Logarithms

• 1. Day 3 Common Logarithms

2. Express each number using exponents. O A. 36 G. 1 O B. 121 What about . . . O C. 4 H. 345 O D. I. 0.0023 O E. 100 O F. 1000 3. Logarithms give you a way to solve for an exponent. O Ex: 5x = 12 Common Logarithms are any logarithm of base 10 Ex: log10 or log 4. Rewriting: 10b = a log10a=b A. 102 = 100 B. 33 = 27 C. 25 = 32 log10 100 = 2 log3 27 = 3 log2 32 = 5 5. E. 641/2 = 8 F. log6 36 = 2 Log64 8 = 1/2 D. 9-2 = 1 81 G. log3 81 = 4 H. log14 = -2 1 196 I. log10 10 = 1 J. Log 1 = 0 Log9 = -2 1 81 62 = 36 34 = 81 101 = 10 100 = 1 14-2 = 1 196 6. Evaluate without a calculator: A. Log4 64 Step 1: set = to x Log4 64 = x Step 2: rewrite in exp. form 4x = 64 Step 3: break down the #s 22x = 26 Step 4: once the bases are the same, set exp. = 2x = 6 x = 3 7. B) Log5 125 5x = 125 5x = 55 x = 5 C) Log4 16 4x = 16 22x = 24 2x = 4 x = 2 8. D) Log343 7 343 = 7x 73x = 71 x = 1/3 Log343 7 = x 3x = 1 9. E) Log3 3x = 3-5 Log3 = x x = -5 243 1 3x = 243 1 243 1 10. Evaluate using a calculator. A) Log 75 1.8751 B) Log -3 Not possible ** log10 (-3) = x 10x = -3 C) Log 1 0 ** log10 1= x 10x = 1 11. But what if the base isnt 10? Use Change of Base Formula: logb a = or 12. A) log5 3 log 3 log 5 = 0.6826 B) log11 18 log 18 log 11 = 1.2054 C) log4 8 log 8 log 4 = 1.5