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Logarithms
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Rational Expression
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100
evaluate: log(4) 2
4^x=2 x=1/2
100
What are the components of a vector with a magnitude of 6 and a direction of 180 degrees?
<-6,0>
100
simplify: tan 4x + 2 tan 2x + 1
( sec 2x ) 2 = sec 4x
100
simplify: 7/4gh + 3/4h^2
(7h+3g)/(4gh^2)
100
Find all factors of: 3x^3 - 2x^2 - 61x -20; x+4
(3x+1)(x-5)
200
If log 4=.602 and log 7=.845 evaluate log7/4
.243
200
What is the direction of a vector with the components <2,3>? what is the magnitude?
directiong=56.3 degrees; mag.= 3.6
200
simplify: 1 / [1 + cos x] + 1 / [1 - cos x]
2 / sin 2x = 2 csc 2x
200
Simplify: 3/(y^2 + y - 12) - 2/(y^2 +6y +8)
x+12/(x+4)(x-3)(x+2)
200
find all zeros of: x^4 - 3x^3 +21x^2 -75x -100
-1, 4, +/- 5i
300
solve: log8 + 2log3
log72=1.86
300
if k=<-2,3> and m=<3,1>, find 2k+3m=?
<5,3>
300
simplify: cos x - cos x sin 2x
cos x cos 2x = cos 3x
300
Simplify: (r+6/r) - (1/r+2) ______________ (r^2 + 4r + 3)/(r^2+2r)
(r+4)/(r+1)
300
find zeros of: x^4 -6x^3 + 6x^2 +24x -40
3+/-i, 2, -2
400
solve: log(10) 3(square root of ten)=x
x=1/3
400
If the components of u are <9.2,-7.7> and the components of v are <6.8,18.8>. what are the components of u+v?
<16,11.1>
400
simplify: csc (x) sin (Pi/2 - x)
csc (x) sin (Pi/2 - x)= csc (x) cos (x) = cot (x)
400
simplify: ((x+1)/5xy)/((x+1)/4x^2y)
4x/5
400
Write the standard form of 5i(13-8i)
40+65i
500
solve: ln(x+7) + ln (x+3)= ln77
x= -14 x= 4
500
Points A(-3,4), B(-1,1), C(4,1), what are the components of vector AC?
<7,-3>
500
simplify: [sin 4x - cos 4x] / [sin 2x - cos 2x]
[sin 2x + cos 2x] = 1
500
simplify: (g^2 +5g+4)/ (5g+5) ___________________ (g^2 +8g +16)/(g^2 +g- 12)
(g-3)/5
500
Write polynomial function with following zeros 5, and squar root of 7
x^3 -5x^2 -7x +35=y