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
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 4.63x + 5 = 1 60 = 1 ()2x = ()-3 3x + 5 = 027
()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

5. Solve 7.log2x3 = 6 26 = x3 (26) = (x3) 22 = x 4 = x
8.log24 + log26= log2x
log224 = log2x
24 = x

6. Solve 9log310-log35=log3x log310 = log3x 5 log32 = log3x 2 = x

7. Solve 11.log(x2 + 21x) = 2 (base 10) 102 = x2 + 21x 100 = x2 + 21x
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

8. Solve 132log23–log2(x + 1)=3 log2( 32 ) = 3 x+1 23 = ( 32 ) 8 = 9_
8 = 9_
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
3x2 +3x = x + 5
3x2 + 2x – 5 = 0
(3x + 5)(x – 1) = 0; x=1

9. Solve 15.log(n+4) =1–log(2n) ln(x + 1) – ln x = ln2
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
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-xlog3=log100
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
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

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
2xlog7+log7=log11
2xlog7=log11–log7
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
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 = s
To do it on the calculator,
type 2 Λ1.3
The “Λ” 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 = -