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## Logarithms

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**Logarithms**the inverse of exponential functions**The logarithmic functions help us work easily with very**large or very small numbers…. While calculators have helped us do this, notice that the LOG and In buttons are STILL a part of the calculator and are still an important part of higher mathematics. Remember how we had to determine the x intercepts for some exponential graphs with trial and error? Logs will deliver us from this!**I like to think of logs as exponents because of the**following…. We must become masters of translating an exponential expression into logarithmic and visa versa. This is what we call “ exponential form”. Let’s change it to “logarithmic form”. log4 64 = 3**Look closely how that translation went…**log464 = 3 The exponent becomes what the log expression is equal to! See why I said logs are equal to exponents. The BASE in the exponential expression becomes the BASE in the logarithmic expression.**You try it!**log232 = 5**You need to translate in the opposite direction too!**log2 = -3**Your calculator will ONLY calculate logs base 10. Log is**called the “common log”. It is so common that when we are referring to log base 10 we don’t include the base. log2 x log5 14 log 14 log x**Your calculator will also calculate logs base e but it uses**a different button. ( In) This log is called the natural log and must be used with e. ln x ln 45**Practice! EVALUATE:**log2 8 It helps to write it into exponential form. log2 8 = x = 8 So 2 to WHAT POWER results in 8?**Practice! EVALUATE:**log36 6 It helps to write it into exponential form. log36 6 = x = 6 So 36 to WHAT POWER results in 6?**Practice! EVALUATE:**log5 0.2 It helps to write it into exponential form. log5 0.2 = x = 0.2 So 5 to WHAT POWER results in 0.2?**Practice! EVALUATE:**125 125 = x = 125**Practice! EVALUATE:**log 100 It helps to write it into exponential form. log 100 = x = 100 So 10 to WHAT POWER results in 100?**Practice! EVALUATE:**it simplifies to 20!**Find the inverse of the function.**Rewrite it in exponential form…. THEN switch the x and y….**Find the inverse of the function.**-3) Rewrite it in exponential form…. THEN switch the x and y…. THEN solve for y**Find the inverse of the function.**-3) + 2 Move the 2 over…. -3) Rewrite it into exponential form…. Switch x and y and solve for y.