Log Equations Review

1
Log Equations Review

• OBJ Review for Quest 2

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

3
Solve

• 3.(?)2x 64
• 27
• (?)2x (?)-3
• 2x -3
• x - ?

• 4.63x 5 1
• 60 1
• 3x 5 0
• x -5
• 3

4
Solve

• 5.log5125 x
• 5x 125
• 5x 53
• x 3

• 6.log?2 t 6
• ?26 t
• (2½)6 t
• 23 t
• 8 t

5
Solve

• 7.log2x3 6
• 26 x3
• (26)? (x3)?
• 22 x
• 4 x

• 8.log24 log26 log2x
• log224 log2x
• 24 x

6
Solve

• 9log310-log35log3x
• log310 log3x
• 5
• log32 log3x
• 2 x

• 10log4(5x 1) 3
• 43 5x 1
• 64 5x 1
• 65 5x
• 13 x

7
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

• 12.2log3(t2 3t 5)
• 32 t2 3t 5
• 9 t2 3t 5
• 0 t2 3t 4
• 0 (t 4)(t 1)
• t 4, -1

8
Solve

• 132log23log2(x 1)3
• log2( 32 ) 3
• x1
• 23 ( 32 )
• x1
• 8 9_
• x1
• 8x 8 9
• 8x 1 x ?

• 14.log(x5) log(3x)
• log(x1)
• log(x5) log(x1)
• 3x
• x 5 x 1
• 3x
• 3x2 3x x 5
• 3x2 2x 5 0
• (3x 5)(x 1) 0 x1

9
Solve

• 15.log(n4) 1log(2n)
• log(n4) log(2n)1
• log10(n4)(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

10
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-xlog3log100
• 5log3-log100 xlog3
• (5log(3)-log(100))
• /log(3)
• x .808

11
Solve. Round answers to 3 dec. places

• 19.log2x 1 log31 x
• (x 1)log2 (1 x)log3
• xlog21log21log3-xlog3
• xlog2xlog3 log3log2
• x(log2log3) log3log2
• log3 log2 x
• log2 log3
• (log(3) log(2))/(log(2) log(3)) x
• .226 x

12
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

13
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

14
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
• 2xlog7log7log11
• 2xlog7log11log7
• x log11 log7
• 2log7
• x

15
Solve. Round answers to 3 dec. places

• 23.log 5 x 3 log 3 2 x
• (x 3)log5(2 x)log3
• xlog53log52log3xlog3
• xlog5xlog32log33log5
• x(log5log3)2log33log5
• 2log3 3log5 x
• log5 log 3
• -.972 x

• 24.log2s 1.3
• 21.3 s
• 2.462 s
• To do it on the calculator,
• type 2 ?1.3
• The ? key is above the
• ? key

16
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

17
Solve. Round answers to 3 dec. places

• 27.log1.2?6 x
• 1.2x ?6
• xlog1.2 log?6
• x log?6
• log1.2
• x 4.914

• 28.log??27 x
• ?x ?27
• 3-x 3?
• x -?