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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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slide1

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

slide2

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.

slide3

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

slide4

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

slide5

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

slide6

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

slide7

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