FAC2bD2-3 Have out: Bellwork: Assignment, pencil, red pen, highlighter, notebook, calculator FAC2bD2-3 Have out: Bellwork: Solve for x. 1) 2) 3) +1 +1 +1 +1 +1 +1 x = 3 +2 x = 5 +1 +2 x – 7 = 0 or x +5 = 0 x = 7 +1 x = –5 +1 Check!!! total: x = 7 +1

The Rules of Exponents: Review Rule: Example: Keyword: 23+5 =28 Product 1) bx+y bx–y 38–5 = 33 Quotient 2) bxy 42(3) = 46 Power 3)

Name parts of a logarithm Argument Base Exponent

Complete the calculations for Part 1a 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 log10( )

1 x • y + The __________ Property of Logarithms multiply log 5 = _________ log 6 = _________ log 30 = _________ log 7 = ________ log 2 = ________ log 14 = ________ log 12 = _________ log 3 = _________ log 36 = _________ When you ________ the arguments, you ______ the exponents. 0.70 0.85 add 0.78 0.30 1.48 1.15 1.08 multiply 0.48 add 1.56 The __________ Property of Logarithms log x + log y = log (________) Conversely: log (x ∙ y) = log (x) ____ log (y) Product x • y +

1c) Practice: Use the property to rewrite each expression as a single logarithm. ii) iii) 1d) Practice: Express in expanded form. i) ii) iii)

The __________ Property of Logarithms 2 divide 1.90 1.75 log 80 = _________ log 8 = __________ log 10 = _________ log 56 = _________ log 8 = _________ log 7 = __________ log 36 = _________ log 4 = __________ log 9 = __________ When you _______ the arguments, you ________ the exponents. subtract 0.90 0.90 1.0 0.85 1.56 divide 0.60 subtract 0.95 The __________ Property of Logarithms log x – log y = log ( ) Conversely: log = log (x) ____ log (y) Quotient x y –

2c) Practice: Use the property to rewrite each expression as a single logarithm. ii) iii) 2d) Practice: Express in expanded form. i) ii) iii)

The ______ Property of Logarithms Conversely: b log a = log (____) 3 Use the product rule! log (52) = log ( ________) = log (____) + log (____) = __________________ log (82) = log ( ________) = log (__) + log (__) = ______________ Write log 63 as the sum of three logs, then simplify: log (63) = log ( ________) = log (__) + log (__) + log (__) Let’s use a calculator: Find: log (34) =________ Find: 4 log 3 = _______ 5 ∙ 5 8 ∙ 8 5 5 8 8 2 log 5 2 log 8 1.91 6 ∙ 6 ∙ 6 1.91 6 6 6 3 log 6 The ______ Property of Logarithms log (ab) = (___)log a Conversely: b log a = log (____) Power b ab

3c) Practice: Use the property to rewrite each expression. ii) iii) 3d) Practice: Rewrite without the coefficients, then simplify. i) ii) iii)

MIXED PRACTICE 1. Rewrite each expression as a single logarithm. Simplify, if possible. a) log 5 + log 7 b) log 15 – log 5 c) log 9 – log 3 log (5 • 7) log 35 log 3 log 3 d) e) 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. b) c) d) e) f)

a) 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. 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.

c) 3. Solve the equations. Check your solutions. 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.

e) 3. Solve the equations. Check your solutions. Use the power property to move the coefficient. e) 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.

g) 3. Solve the equations. Check your solutions. Use the power property to move the coefficient. g) 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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