Common Logarithms
Download as PPTX, PDF1 like981 views
This document discusses common logarithms and how to evaluate logarithmic expressions with and without a calculator. It provides examples of rewriting exponential expressions as logarithmic expressions by setting them equal to variables and manipulating the equations. It also introduces the change of base formula for evaluating logarithms with bases other than 10.
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 isn’t 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