Precalc wup 410 11 Write the equation loge

11. 5 Common Logarithms A common logarithm is a logarithm with a base of

Use your properties of logarithms to simplify. Remember a logarithm is an exponent. l

The antilog… l l l exponent The inverse of a logarithm is a _______

Change of base – we want base 10 then we can use our calculators.

Use logs to solve exponential functions. . l Ex 4: solve 63 x =

Ex 5: 12 x-4 = 3 x-2 l Take the log of both sides,

Ex 6: graph y= 3 log(x+1) l What is the basic shape of a

Remember: l Logs in real number system are undefined for negative numbers. l You

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Pre-calc w-up 4/10 -11 Write the equation loge 13. 7 = x in exponential form 2. Write the equation (1/4)-4 = 256 in log form 3. Evaluate the expression log 443 4. Solve log 2 x + log 210 = log 270 1.

11. 5 Common Logarithms A common logarithm is a logarithm with a base of 10. q log 10 x = logx q

Use your properties of logarithms to simplify. Remember a logarithm is an exponent. l Ex l 1: Given log 8 = 0. 9031 evaluate A) log 800, 000 = log (100, 000 x 8) = log 105 + log 8 = 5 + 0. 9031 = 5. 9031

The antilog… l l l exponent The inverse of a logarithm is a _______ So if log x = a then ____ 10 a = x What… 1. 06069784 – push the buttons on your calc Log 11. 5=_____ 11. 5 on calc push Antilog 1. 06069784 = _______ 2 nd log 10^1. 06069784 (inverse of log) Try these l Answers l 2 a) log 54. 1 1. 7332 2 b) antilog 1. 9484 88. 7973

Change of base – we want base 10 then we can use our calculators. l a, b, n are positive and a and b don’t equal 1 then the change of base formula is… l Ex 3: find the value of log 9 1043

Use logs to solve exponential functions. . l Ex 4: solve 63 x = 81 l Take the log of both sides l log 63 x = log 81 l “finding answers in the hunt powers of log can go up front” 3 x log 6 = log 81 (now solve) l 3 x = log 81/log 6 (divided both sides by log 6) l x =. 8175 (divided both sides by 3) l

Ex 5: 12 x-4 = 3 x-2 l Take the log of both sides, bring powers up front l (x – 4)log 12 = (x – 2) log 3 l You can NOT distribute the log, a log is an exponent l Do you do this (x + 5)2 = x 2 + 25 l Divide by a log 1 st, (doesn’t matter which one) then follow rules of solving. NO x = 5. 58

Ex 6: graph y= 3 log(x+1) l What is the basic shape of a logarithm? Type it into your calc y = logx l How does that compare to y = 10^x? l l Plug into your calculator, adjust window, label at least 3 points.

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