Training Camp (cont 3)

Read pages 430-432 Examples 3, 4, and 5 in your textbook, Principles of Mathematics 12. Complete the Your Turn questions on pages 430, 431 and 432 for more practice evaluating logarithmic expressions without technology. Click here to verify your answers.

Watch the following three videos to see more examples. Evaluate Common Logarithms Without a Calculator Evaluate Logarithms Without a Calculator - Whole Numbers Evaluate Logarithms Without a Calculator - Fractions

As mentioned in Warm Up, logarithmic scales are used often to display numeric values that represent natural phenomena. In Chemistry, a very important quantity is the concentration of hydrogen ions, written as [H⁺], which is related to the acidity of a liquid. In a normal pond, the concentration of hydrogen ions is about 10^-6 moles per litre. This means that every litre of water has about 10^-6, or , moles of hydrogen ions.

Acidity of a liquid usually is not measured as concentration because numbers such as are very cumbersome. Instead, acidity is measured as pH, an abbreviation of potential of hydrogen. Hydrogen is present in water and in all organic compounds, but pH is not something seen or felt. pH is a measure of acidity or alkalinity.

A common example of measuring pH occurs at any swimming pool. Water testing is a vital aspect of maintaining a pool in terms of health and hygiene. Not only is dirty water unpleasant to swimmers, it can result in illness and cause horrible skin irritations and eye infections. For this reason, testing all pool water regularly is important to ensure that the swimming pool pH levels are correct.

Swimming pool pH levels determine how acidic or alkaline the water in a pool is at any one time. This is tested by using the universal pH scale, which is a logarithmic number scale (from 0 to 14) that shows the strength of an acid or alkali. The closer to zero on the scale, the more acidic a substance is.