Assignment pencil red pen highlighter notebook calculator Solve
Assignment, pencil, red pen, highlighter, notebook, calculator Solve for x. 1) 2) x = 5 +2 3) +1 +1 x=3 total: +2 +1 +1 x – 7 = 0 or x +5 = 0 +1 x = – 5 +1 x = 7 +1 Check!!! x = 7 +1
w ev ie R Rule: 1) 2) 3) Example: bx+y bx–y bxy 23+5 =28 38– 5 = 33 42(3) = 46 Keyword: Product Quotient Power
Argument Base Exponent
Complete the calculations for Part 1 a on your calculator. Be sure to locate the LOG function on your calculator. LOG button Note: the LOG function on your calculator is base 10, that is: log( ) means log 10( )
ly ltip mu 0. 85 log 7 = ____ 0. 30 log 2 = ____ 1. 15 log 14 = ____ 1. 08 log 12 = _____ 0. 48 log 3 = _____ 1. 56 log 36 = _____ multiply the When you ____ add arguments, you ______ the exponents. d ad log 5 = _____ 0. 70 log 6 = _____ 0. 78 log 30 = 1. 48 _____ Product Property of Logarithms The _____ x • y log x + log y = log (____) Conversely: log (x ∙ y) = log (x) ____ + log (y)
1 c) Practice: Use the property to rewrite each expression as a single logarithm. i) iii) 1 d) Practice: Express in expanded form. i) iii)
ide log 36 = _____ 1. 56 0. 60 log 4 = _____ log 9 = _____ 0. 95 1. 75 log 56 = _____ 0. 90 log 8 = _____ 0. 85 log 7 = _____ ct tra div b su 1. 90 log 80 = _____ 0. 90 log 8 = _____ 1. 0 log 10 = _____ divide When you _______ the subtract the arguments, you ____ exponents. The _____ Quotient Property of Logarithms x log x – log y = log ( ) y – log (y) Conversely: log = log (x) ____
2 c) Practice: Use the property to rewrite each expression as a single logarithm. i) iii) 2 d) Practice: Express in expanded form. i) iii)
Use the product rule! log (52) = log ( ____) log (82) = log ( ____) 5 ∙ 5 8 ∙ 8 8 5 5 + log (____) 8 + log (__) = log (__) 2 log 8 2 log 5 = _________ = _______ Write log 63 as the sum of three logs, Let’s use a calculator: 1. 91 then simplify: Find: log (34) =____ 6∙ 6∙ 6 1. 91 log (63) = log ( ____) Find: 4 log 3 = _______ 6 6 + log (__) = log (__) 3 log 6 = _________ Power Property of Logarithms The ______ log (ab) = (___)log a b ab Conversely: b log a = log (____)
3 c) Practice: Use the property to rewrite each expression. i) iii) 3 d) Practice: Rewrite without the coefficients, then simplify. i) iii)
MIXED PRACTICE 1. Rewrite each expression as a single logarithm. Simplify, if possible. a) log 5 + log 7 log (5 • 7) log 35 b) log 15 – log 5 c) log 9 – log 3 d) e) log 3 f)
MIXED PRACTICE 1. Rewrite each expression as a single logarithm. Simplify, if possible. g) h) i) j) k) l)
2. Express in expanded form. a) b) c) d) e) f)
3. Solve the equations. Check your solutions. To solve problems such as this, we need to use the product property to put the logs on the left side together. a) Now the problem is written: log ( ) = log ( ) Use the property of equality to set the arguments equal, then solve. We are going to work on the problems in the first column. Skip to part (c) now.
3. Solve the equations. Check your solutions. c) Use the quotient property to combine the left side. Now the problem is written: log ( ) = log ( ) Use the property of equality to set the arguments equal, then solve.
3. Solve the equations. Check your solutions. e) Use the power property to move the coefficient. Use the quotient property to combine the right side. Now the problem is written: log ( ) = log ( ) Use the property of equality to set the arguments equal, then solve.
3. Solve the equations. Check your solutions. g) Use the power property to move the coefficient. Use the product property to combine the right side. Now the problem is written: log ( ) = log ( ) Use the property of equality to set the arguments equal, then solve.
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