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.

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Presentation transcript:

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

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

Ex 1: Given log8 = 0.9031 evaluate 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

The antilog… 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 exponent 10a = x 1.06069784 – push the buttons on your calc 11.5 on calc push 2nd log 10^1.06069784 (inverse of log)

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

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)

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 

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.

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