Log Equations Review

OBJ: Review for Quest 2

Solve

1.162 – s 2 = ½

24(2 – s 2) = 2-1

4(2 – s2) = -1

8 – 4s2 = -1

9 – 4s2 = 0

(3 – 2s)(3 + 2s) = 0

s =

2.64x – 4 = (½)2x

26(x – 4 ) = (2-1)2x

6(x – 4) = (-1)2x

6x – 24 = -2x

8x = 24

x = 3

Solve

3.()2x = 64

27

()2x = ()-3

2x = -3

x = -

4.63x + 5 = 1

60 = 1

3x + 5 = 0

x = -5

3

Solve

5.log5125 = x

5x = 125

5x = 53

x = 3

6.log2 t = 6

26 = t

(2½)6 = t

23 = t

8 = t

Solve

7.log2x3 = 6

26 = x3

(26) = (x3)

22 = x

4 = x

8.log24 + log26= log2x

log224 = log2x

24 = x

Solve

9log310-log35=log3x

log310 = log3x

5

log32 = log3x

2 = x

10log4(5x – 1) = 3

43 = 5x – 1

64 = 5x – 1

65 = 5x

13 = x

Solve

11.log(x2 + 21x) = 2

(base 10)

102 = x2 + 21x

100 = x2 + 21x

0 = x2 + 21x – 100

0 = (x + 25)(x – 4)

x = 4, -25

12.2=log3(t2 – 3t + 5)

32 = t2 – 3t + 5

9 = t2 – 3t + 5

0 = t2 – 3t – 4

0 = (t – 4)(t + 1)

t = 4, -1

Solve

132log23–log2(x + 1)=3

log2( 32 ) = 3

x+1

23 = ( 32 )

x+1

8 = 9_

x+1

8x + 8 = 9

8x = 1: x = ⅛

14.log(x+5) – log(3x) =

log(x+1)

log(x+5) = log(x+1)

3x

x + 5 = x + 1

3x

3x2 +3x = x + 5

3x2 + 2x – 5 = 0

(3x + 5)(x – 1) = 0; x=1

Solve

15.log(n+4) =1–log(2n)

log(n+4) +log(2n)=1

log10(n+4)(2n) = 1

101 = (n + 4)(2n)

2n2 + 8n – 10 = 0

2(n2 + 4n – 5) = 0

2(n + 5)(n – 1) = 0

n = 1

16.ln is the same as loge

ln(x + 1) – ln x = ln2

ln x + 1 = ln2

x

x + 1 = 2

x

2x = x + 1

x = 1

Solve. Round answers to 3 dec. places

17.2x = 5

log2x = log5

x log2 = log5

x = log5

log2

x = log(5)/log(2)

x = 2.322

18.35 – x = 100

log35 – x = log100

(5 – x)log3 = log100

5log3-xlog3=log100

5log3-log100= xlog3

(5log(3)-log(100))

/log(3)

x = .808

Solve. Round answers to 3 dec. places

19.log2x +1 = log31 – x

(x + 1)log2 = (1 – x)log3

xlog2+1log2=1log3-xlog3

xlog2+xlog3 = log3–log2

x(log2+log3) = log3–log2

log3 – log2 = x

log2 + log3

(log(3) – log(2))/(log(2) + log(3)) = x

.226 = x

Solve. Round answers to 3 dec. places

20.ex = 4

log ex = log 4

x log e = log 4

x = log 4

log e

x = 1.386

20.ex = 4

ln ex = ln4

x ln e = ln4

x = ln4

x = 1.386

Solve. Round answers to 3 dec. places

21.3e2x – 1 = 12

e2x – 1 = 4

log e2x – 1 = log 4

(2x – 1) log e = log4

2xlog e-log e = log4

x = log e + log 4

2 log e

= 1.193

21.3e2x – 1 = 12

e2x – 1 = 4

ln e2x – 1 = ln4

2x – 1= ln4

2x = 1 + ln4

x = 1 + ln4

2

= 1.193

Solve. Round answers to 3 dec. places

21.3e2x – 1 = 12

e2x – 1 = 4

ln e2x – 1 = ln4

2x – 1= ln4

2x = 1 + ln4

x = 1 + ln4

2

= 1.193

22.72x + 1 = 11

log72x + 1 = log 11

(2x + 1)log7= log11

2xlog7+log7=log11

2xlog7=log11–log7

x = log11 – log7

2log7

x =

Solve. Round answers to 3 dec. places

23.log 5 x +3 = log 3 2 – x

(x + 3)log5=(2 – x)log3

xlog5+3log5=2log3–xlog3

xlog5+xlog3=2log3–3log5

x(log5+log3)=2log3–3log5

2log3 – 3log5 = x

log5 + log 3

-.972 = x

24.log2s = 1.3

21.3 = s

2.462 = sTo do it on the calculator,

type 2 Λ1.3

The “Λ” key is above the

“” key

Solve. Round answers to 3 dec. places

25.log812 = x

8x = 12

xlog8 = log12

x = log12

log8

x = log(12)/log(8)

x = 1.195

26.log53.6 = x

5x = 3.6

xlog5 = log3.6

x = log3.6

log5

x = log(3.6)/log(5)

x = .796

Solve. Round answers to 3 dec. places

27.log1.26 = x

1.2x = 6

xlog1.2 = log6

x = log6

log1.2

x = 4.914

28.log27 = x

x = 27

3-x = 3

x = -