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Mathematics for Technology II (Math 2131)

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Study Force Academy
Durham College, Mathematics
Free
  • 36 lessons
  • 0 quizzes
  • 14 week duration

Rules of Logarithms

Since a logarithmic function is technically the inverse of an exponential function, it must follow the laws of exponents. The three properties of logs listed below will be used to combine and solve expressions and equations in this section and the next. Each of these properties are derived from the laws of exponents.

Log of a Product logbM·N=logbM+logbN
Log of a Quotient logbMN=logbMlogbN
Log of a Power logbMp=p·logbM

We’ll being our focus with first of three properties: log of a product.

log (7x) → For this, notice that 7 and ‘x’ are products; hence, they can be written separately as the sum of two logs → log 7 + log x

log 3 + log x + log y → Notice that there are three terms all containing log of base 10. This means we can write 3, x, and y as products under one log → log 3xy

The next few examples pertain to the We’ll being our focus with first of three properties: log of a product.

 

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