Logarithmic FunctionsThe inverse of the equation y = bx is x = by Since there is no algebraic method for solving x = by for y in terms of x, the Logarithmic Function is used to allow y to be expressed in terms of x.Thats right! Interchange x and y.Sounds pretty easy so far. Lets move on.

Lets Take a Closer Look at Some LogsA logarithm is really an exponent written in a different form.The equation y = bx is an exponential functionLets break this down.b is the basex is the exponenty is the value of bxNow lets bring in the logs.Written in logarithmic form, the equation y = bx would bex = log b aWe read this asx is the logarithm of a with base b

Breaking Down LogsLets look at a log piece by piece.The equation x = log b ais a logarithmic functionLets break this down.b is the basex is the exponenta is the value of bxHey! Ive seen this before.Its Sam Tingas breaking down exponential functions.That was easy

Comparing Logarithmic form and exponential formExponential FormLogarithmic Formy = bxx = log b a32 = 255 = log 2 32512 = 833 = log 8 5124 = log 3 813 = log 5 12581 = 34125 = 53AsiDeFacil

Logarithms with Variables3 = log 4 aIn each equation, find the value of the variablesince 43 = 64, a = 64x = log 6 36since 62 = 36,x = 23 = log b 125since 53 = 125,b = 5Hey, I can just use my calculator for this.This looks a little harder. Maybe I should use a real calculator for this one.That was easy43 = a6x = 36b3 = 125

More Logarithms with VariablesIn each equation, find the value of the variable5 = log 8 asince 85 = 32,768, a = 32,768x = log 7 2,401since 74 = 2,401,x = 43 = log b 6,859since 193 = 6,859,b = 19Hey, those are some pretty big numbers. I hope my calculator knows how to do this.That was easy85 = a7x = 2,401b3 = 6,859

Common LogsAny logarithm with base 10 is a Common LogWhen writing a common logarithm, the base is usually omitted.So, 5 = log 10 100,000 and 5 = log 100,000 are Sam Ting. Lets compare Logarithmic Form and Exponential Form of some Common Logs.Exponential FormLogarithmic Form3 = log 1,0001,000 = 1031,000,000 = 1066 = log 1,000,00010,000 = 1044 = log 10,000That was easy

Common Logs with VariablesIn each equation, find the value of the variablex = log 10010x = 100since 102 = 100, then x = 2count the zeros7 = log a107 = asince 107 = 10,000,000, then a = 10,000,000write the proper number of zeros Hey, I dont even need a calculator for this!That was easy

More Common Logs with VariablesFind the value of the variable to the nearest one hundredthx = log 1,34510x = 1,345Hey, theres no zeros to count.2.865 = log a102.865 = aThat was easyWe could use the LOG key on our calculator.LOG (1,345) = 3.13Whats the proper number of zeros?We could use the 10x key on our calculator.102.865 = 732.82

Change of BaseHow can I get my calculator to evaluate logs in bases other than base 10?Thats easy, just use the Change of Base Formulax = log 8 512= 3x = log 12 248,832= 5Its time to push the easy button once again!

More Change of BaseLets throw some decimals into the mix.x = log 4 32x = log 4.5 91.125= 3= 2.5This stuff is too easy. Soon Ill have to buy new batteries for my easy button.x = log 8.125 1,986.597= 3.625That was easy