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 10.4 Properties of Logarithms Objectives: The student will be able to… 1) Solve exponential equations using common logarithms. 2) Evaluate logarithmic expressions using the Change of Base Formula.

Common Logarithms - We can use the base 10 logarithm function in many applications. - Base 10 logarithms are called common logarithms. - Instead of writing log 10 x can be written log x

Example 1 Write each equation in logarithmic form: a) b) c) d) Evaluate log 10,000

Sometimes an application of logarithms requires that you use the inverse of logarithms, or exponentiation Application: Earthquakes The amount of energy E, in ergs, that an earthquake releases is related to its Richter scale magnitude M by the equation logE = M. The Chilean earthquake of 1960 measured 8.5 on the Richter scale. How much energy was released?

Change of Base Formula For all positive numbers a, b and n, where and, Example:

Example 2 Express log 4 25 in terms of common logarithms. Then approximate its value to four decimal places.

Example 3 Solve Exponential Equations using Logarithms:

You Try It… Solve Exponential Equations using Logarithms:

Application: Interest If you deposit P dollars into a bank account paying an annual interest rate r (expressed as a decimal), with n interest payments each year, the amount A you would have after t years is Marta places $100 in a savings account earning 6% annual interest, compounded quarterly. a) If Marta adds no more money to the account, how long will it take the money in the account to reach $125? b) How long will it take for Marta’s money to double?

Application: pH Find the pH of each substance given its concentration of hydrogen ions: a) Ammonia [H+] = 1 x mole per liter b) Vinegar [H+] = 6.3 x mole per liter c) Lemon juice [H+] = 7.9 x mole per liter

Partner Practice You Try It… Text p. 549 #s 7, 9-11, 13-16

Homework Text p. 550 all equations from #s #s all