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Lo g arithms – makin g com p lex calculations eas y

Lo g arithms – makin g com p lex calculations eas y. John Napier. John Wallis. Johann Bernoulli. Jost Burgi. Lo g arithms. Index Power Exponent Lo g arithm. Base. Number. 10 2 = 100. “10 raised to the power 2 gives 100”.

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Lo g arithms – makin g com p lex calculations eas y

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  1. Logarithms – making complex calculations easy John Napier John Wallis Johann Bernoulli Jost Burgi

  2. Logarithms Index Power Exponent Logarithm Base Number 102 = 100 “10 raised to the power 2 gives 100” “The power to which the base 10 must be raised to give 100 is 2” “The logarithm to the base 10 of 100 is 2” Log10100 = 2

  3. Logarithms y = bx Logby = x Logarithm logby = x is the inverse of y = bx Base Number 102 = 100 Logarithm Base Log10100 = 2 Number

  4. Laws of logarithms Every number can be expressed in exponential form… every number can be expressed as a log Let p = logax and q = logay So x = apand y = aq xy = ap+q p + q = loga(xy) p + q = logax + logay = loga(xy) loga(xy) = logax + logay

  5. Laws of logarithms Every number can be expressed in exponential form… every number can be expressed as a log Let p = logax and q = logay So x = apand y = aq xy = ap-q p - q = loga(x/y) p - q = logax - logay = loga(x/y) loga(x/y) = logax - logay

  6. Laws of logarithms Every number can be expressed in exponential form… every number can be expressed as a log Let p = logax and q = logax So x = apand x = aq x2 = ap+q p + q = loga(x2) p + q = logax + logax = loga(x2) logaxn = nlogax

  7. Laws of logarithms Every number can be expressed in exponential form… every number can be expressed as a log loga(xy) = logax + logay am.an = am+n loga(x/y) = logax - logay am/an = am-n logaxn = nlogax (am)n = am.n

  8. Change of base property Logbx Logax = Logba

  9. Solving equations of the form ax = b 3x = 9 4x = 64 5x = 67 Solve by taking logs: log5x = log67 xlog5 = log67

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