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Pre-calc w-up 4/10-11

Pre-calc w-up 4/10-11. Write the equation log e 13.7 = x in exponential form Write the equation (1/4) -4 = 256 in log form Evaluate the expression log 4 4 3 Solve log 2 x + log 2 10 = log 2 70. 11.5 Common Logarithms. A common logarithm is a logarithm with a base of 10. log 10 x = logx.

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Pre-calc w-up 4/10-11

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  1. Pre-calc w-up 4/10-11 • Write the equation loge 13.7 = x in exponential form • Write the equation (1/4)-4 = 256 in log form • Evaluate the expression log443 • Solve log2x + log210 = log270

  2. 11.5 Common Logarithms A common logarithm is a logarithm with a base of 10. log10x = logx

  3. Use your properties of logarithms to simplify. Remember a logarithm is an exponent. • Ex 1: Given log8 = 0.9031 evaluate • A) log 800,000 = log (100,000 x 8) = log 105 + log 8 = 5 + 0.9031 = 5.9031

  4. The antilog… exponent • The inverse of a logarithm is a _______ • So if log x = a then ________ • What… • Log 11.5=_________ • Antilog 1.06069784 = _____________ • Try these 2a) log 54.1 2b) antilog1.9484 • Answers 1.7332 88.7973 10a = x 1.06069784 – push the buttons on your calc 11.5 on calc push 2nd log 10^1.06069784 (inverse of log)

  5. Change of base – we want base 10 then we can use our calculators. • a,b,n are positive and a and b don’t equal 1 then the change of base formula is… • Ex 3: find the value of log9 1043

  6. Use logs to solve exponential functions.. • Ex4: solve 63x = 81 • Take the log of both sides • log63x = log 81 • “finding answers in the hunt powers of log can go up front” • 3x log 6 = log 81 (now solve) • 3x = log81/log6 (divided both sides by log6) • x = .8175 (divided both sides by 3)

  7. Ex 5: 12x-4 = 3x-2 • Take the log of both sides, bring powers up front • (x – 4)log12 = (x – 2) log3 • You can NOT distribute the log, a log is an exponent • Do you do this (x + 5)2 = x2 + 25 NO • Divide by a log 1st, (doesn’t matter which one) then follow rules of solving. x = 5.58 

  8. Ex6: graph y= 3log(x+1) • What is the basic shape of a logarithm? • Type it into your calc y = logx • How does that compare to y = 10^x? • Plug into your calculator, adjust window, label at least 3 points.

  9. Remember: • Logs in real number system are undefined for negative numbers. • You can get a negative answer, you can’t take a log of a negative number • Homework: pg 730 # 19-21,23,28 – 45 all • 19-23 NO CALC • 28-rest you can use a calculator

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