Intermediate Algebra

Problem solving
460-61 3,11,17,19,27,33,39,41,49Question 3 Writing in logarithmic form
45=1024
Baselog=number
In this case
Log4 1024= 5
Question 11
8-2/3=1/4
Log8 ¼=-2/3
Question 17 (writing in exponential form)
Log101/10000 =-4
In power form it will be
10-4=1/10000
Question 19
Log 100100=1
=1001=100
Question 27 (Matching logarithm with its answer).
Log88=1
Log161=0.5
Log0.31=0
Log √7√7=-1
Question 33 (solving the problem)
Logx125=-3
X-3=53
Given the reciprocal of one power is equal to the other power
Then 1/x=5
And x=1/5
Question 39
Logx1/25=-2
x-2=5-2
Powers are equal and therefore bases are equal to
x=5
Question 41
Log232=x
2x=32
2x=25
x=5
Question 49
62-63 7, 11, 17,21,27,31,33,41,43
Question 7
Log7(4-5)
=Log74-Log75
Question 11
Log462
2log46 or in summation form
=Log46 +Log46
Question 17
Log2(3√x*3√y)/r2
Log 2(X1/3*y1/3)/r2
1/3log2x +1/3 Log2y -2Log2r
Question 21
Logbx+Logby=Logb(x*y)
Question 27
3Log35-4Loga3
Log353-Log334
Loga(53/34)
Question 31
3Logy x +Logyy-3/2 Logyz-3Logya
Logyx3+Logyy –Logz3/2-Logya3
Logy{(x3*y)/(z3/2*a3)
Question 33
Log1018=x
10x=18
10x=101.25527
X=1.25527
Question 41
Log103=x
10x=3
10x=100.4771
X=0.4771
Question 43
Log1095
5(Log109=x)
5(10x=9)
5{10x=100.9542)
X=0.9542
=5*0.9542
=4.7712
64,65,66 7, 13,19,39,47, 53
Question 7
Finding logarithm
Log 43
The common base is 10
Therefore 10x=43
10x=101.6335
x=1.6335
Question 13
Log 457.2
Log(4.572*100)
Log4.572 +Log 102
=0.6601+2
=2.6601
Question 19
Ln388.1
=Ln(3.881*102)
=Ln3.881+Ln102
=ln3.881+e2
=5.

9613
Question 39
Log 4x-log(x-3)=log 2
(4x/(x-3))=2
4x=2x-6
2x=6
X=3
Question 47
Principal =2000
Time =6yrs
Quartery at 4%
Amount=p(1+r/4)6*4
=2000(1+0.01)24
=2000(1.2697)
=2539.4
Question 53
Amount= 51850
rate 6.5%
time 40 yrs51850=P(1+0.065)40
51850=P(1.065)40
P=51850/(1.065)40
=4176