1. a. i. -5log749+4log55-6log42
=-5log777+4log5512-6log4412
=-(5)(7)log77+412log55-612log44
=-571+4121-6121
=-35+2-3=-36
ii.log7343x16807y
=log7343x-log716807y
=log773x-log775y
=3xlog77-7ylog77
=3x-7y
b. 122×5×3-71024 ×5-3-2
=12-4×5-2×3141024-22×56=4-4×3-4×3141024-1×56+2=2-8×3102-10×58=3102-10+8×58=2231058
c. The graph is shown in the next figure:
2 a. 2x=1024
2x=210→x=10
i. 7292x-3=6561
362x-3=38
62x-3=8
12x-18=8
12x12=2612→x=136
iii. log23x+1=4
3x+1=24
3x+1=16
3x3=153→x=5
b. The slope of the line 2x+y=4 is:
y=-2x+4→m=-2
The equation of the line passing through (-1,4) parallel to 2x+y=4 is:
y-y1=mx-x1→y-4=-2x--1
y-4=-2x-2→y=-2x+2
c. i. -35w2
=-3w25
ii. 5c3225c-11
=5c3+113252=c133252-1 =c139×5=c1345
iii. 2xx73∙7x
=x12x73x17=x12-73-17=x21-98-642=x-8342=1x8342
3. a. The graph of y=2x2-7x+12 is:
Intersection with the y-axis is at (0,12). The curve does not intersect the x-axis.
b. i. x2+2x-143=0
x+13x-11=0→x=-13, 11
ii. x2-225→(x+15)(x-15)
c. 2y+10x=14;y=x2-10x-7
Isolating y from 2y+10x=14:
2y=14-10x→y=7-5x
Substituting to the next equation:
7-5x=x2-10x-7
x2-10x+5x-7-7=0
x2-5x-14=0
x-7x+2=0→x=7,-2
4. a. 1-3x5
=15+514-3x+1013-3x2+1012-3x3+51-3x4+-3x5
=1-15x+90x2-270x3+405x4-243x5
b. 1-2x7
The x6 term is:
61-2x6=664x6=384x6→384
c. n3=6n2
n!n-3!3!=6n!n-2!2!
n!n-3!3×2!×3×2!n!=6n!n-2!2!×3×2!n!
1n-3!n-3!=18n-2n-3!n-3!
1=18n-2 →n-2=18→n=20
