# Mathematics for Technology II (Math 2131)

Durham College, Mathematics
Free
• 36 lessons
• 0 quizzes
• 14 week duration
• ##### Solving Systems of Equations

This unit introduces how to systematically solve a system of equations, namely linear equations. Examples of non-linear systems, including systems of 3 unknowns will be of emphasis.

• ##### Graphs of Trigonometric Functions

The unit focuses primarily on how to graph periodic sinusoidal functions, and how to identify features of a waveform to produce an equation by inspection.

• ##### Polar Coordinate Functions

An introduction to the polar coordinate system.

• ##### Complex Numbers

This unit is an extension of what was introduced in Math 1131. To learn how to work with radicals, knowing your exponent laws in crucial. Hence, this unit begins with a thorough review.

• ##### Logarithmic Functions

This chapter introduces you to exponential functions, and how they can be solved using logarithms.

• ##### Trigonometric Identities and Equations
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• ##### Analytic Geometry
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## Mathematics for Technology II (Math 2131)

### 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 ${\mathrm{log}}_{b}\left(M·N\right)={\mathrm{log}}_{b}M+{\mathrm{log}}_{b}N$ Log of a Quotient ${\mathrm{log}}_{b}\frac{M}{N}={\mathrm{log}}_{b}M–{\mathrm{log}}_{b}N$ Log of a Power ${\mathrm{log}}_{b}{M}^{p}=p·{\mathrm{log}}_{b}M$

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.