Properties of Logarithms -- Section 4.5 --

 Definition of Logs log b x = y  Û x = b y A logarithm is an exponent.

 Write in terms of x, y, and z. *
 We want to write the expression such that the variables are as isolated as possible. Solve Step Property Start with division  division turns into subtraction =  log 3 + log x - (log y + log z) Take care of multiplication next  multiplication turns into addition log b MN = log b M + log b N =  log 3 + log x - log y - log z Distribute the minus sign Recall: log  x = log 10 x All variables are isolated * Assume all values for x, y, and z are defined for each expression. Example log (-2) is undefined.

 Write in terms of the logarithms  of x, y, and z.
 [Solution]
 Write in terms of the logarithms  of x, y, and z.

 We want to write the expression such that the variables are as isolated as possible. Solve Step Property Start with division  division turns into subtraction Recall: Convert radicals into exponents Replace radicals Exponents turn into multiplication log b M p  = p log b M Take care of multiplication next  multiplication turns into addition log b MN = log b M + log b N Do  log b x2 = 2 log b x next log b M p  = p log b M Distribute 1/3 through ( ) All variables are isolated * Assume all values for x, y, and z are defined for each expression. Example log (-2) is undefined.

 Write in terms of the logarithms  of x, y, and z.
 [Solution]
 Evaluate the following to 3 decimals places:    log 2 5
 Solve Step Property Change of Base formula HINT: use these key strokes log 5 ÷ log 2 [enter or =]
 Evaluate the following to 3 decimals places:    log 5 2
 [Solution]

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