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1) Solve: log 27 x=-2/3

1) Solve: log 27 x=-2/3. 2) Write in logarithmic form: 49 1/2 = 7. 3) Graph y = -2(3) -x. x= 27 -2/3 x =. 2) ½ = log 49 7. 3) = -2(1/3) x. a 3 a 5 = a 3+5. log a 3 + log a 5 = log a (3*5). (a 3 ) 5 = a 3*5. 5log a 3 = log a 3 5. a 5 = a 5-3 a 3.

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1) Solve: log 27 x=-2/3

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  1. 1) Solve: log27x=-2/3 2) Write in logarithmic form: 491/2 = 7 3) Graph y = -2(3)-x • x= 27-2/3 • x = 2) ½ = log497 3) = -2(1/3)x

  2. a3a5 = a3+5 loga3 + loga5 = loga(3*5) (a3)5 = a3*5 5loga3= loga35 a5 = a5-3 a3 loga5 – loga3 = loga (5/3) a0 = 1 Loga1=0 ax is always positive Loga(~) ~ is always positive!! Adding logs, Adding logs, you multiply them A number in front of log becomes the exponent. Minus logs, minus logs, you divide them Log of 1 is zero, and can’t take log of negative.

  3. Recall that if logx5 = logxy then 5=y logx25 = 2 then 25 = x2 Goal is to condense logs to just ONE LOG on each side…. 13) log45 + log4x = log460 24) log2(x+4) – log2(x-3)= 3 Log45x = log460 5x = 60 x = 12 CHECK answer! {12} 18) 3 log82 – log84 = log8b log823– log84 = log8b 8(x-3) = x+4 8x-24=x + 4 7x = 28 x=4 CHECK! {4} log8(8/4) = log8b Log82 = log8b 2 = b Problems taken from Glencoe Algebra II workbook 10.3

  4. 12) 3log74=2 log7b 11) log1027 = 3 log10 x log743 = log7b2 log764 =log7b2 64 = b2 + 8 = b {8} Log1027 = log10x3 27 = x3 3 = x {3} Problems taken from Glencoe Algebra II workbook 10.3

  5. 16) Log2q – log23 = log27 15) log5y-log58=log51 Log2 (q/3)= log27 q/3 = 7 q = 21 {21} Log5 y/8 = log5 1 y/8 = 1 y = 8 {8} Problems taken from Glencoe Algebra II workbook 10.3

  6. 21) log3d + log33 = 3 23) log2s + 2 log25=0 Log2s + log252 = 0 Log2(s25) = 0 25s = 20 25s = 1 s = 1/25 Log3 (d3) = 3 3d = 33 3d = 27 d = 9 Problems taken from Glencoe Algebra II workbook 10.3

  7. 19) log4x+ log4(2x – 3) = log42 20)log10x + log10(3x – 5) = 2 Log10(x(3x-5)) = 2 3x2 – 5x = 102 3x2 – 5x = 100 3x2 – 5x – 100 = 0 (3x -20 )(x+5 )=0 x = 20/3 x = -5 {20/3} Log4 (x(2x -3)) = log4(2) 2x2 – 3x = 2 2x2 – 3x – 2 = 0 (2x + 1)(x – 2) = 0 2x + 1= 0 x-2=0 x = -1/2 x =2 {2} Problems taken from Glencoe Algebra II workbook 10.3

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