Inverses, Composite Functions, and Random
Expanding and Condensing Logarithms
Products and Factors of Polynomials
Evaluating Logarithms and Exponential Equations
Exponentials / Logarithms
Radical Equations
Rational Expressions
100
Solve using the quadratic equation
3y^2=1-y
What is
(-1+-sqrt(13))/6
100
Use the properties of logarithms to write each of the following as a single logarithm. SIMPLIFY!
3log5x-log54
log5(x3/4)
100
Simplify
-3(x^2-2)+2(3-2x^2)
What is
-7x^2 + 12
100
Evaluate the following log.
log216
4
100
Change the logarithm into exponential form.
Log3(27)=3
What is 33=27
100
Solve the equation:
sqrt(x)+2=6
What is 16
100
Simplify:
(2(x+3)*(x-4)) / ((x-4)*(x+3))
What is 2
200
Find the inverse.
200
Completely expand the following logarithms. (Answers have no exponents, multiplication or division)
log4(20/x3)
log420 - 3log4x
200
Find the Least Common Multiple (LCM) of
12a^2b^2, 8ab^3, 16b^4
What is
48a^2b^4
200
Evaluate the following log.
log4(1/64)
-3
200
Rewrite the following function in exponential form.
log81=0
80=1
200
Solve for x
2sqrt(x+1)=14
What is
x = 48
200
Simplify:
(2x)/5 divide (6x^2)/5
What is
1/(3x)
300
Given the functions h(x) = 2x - 6 and g(x) = x+ 4
What is h(g(x))
h(g(x)) = 2(x+4) - 6
= 2x +8 -6
= 2x + 2
300
Use the properties of logarithms to write each of the following as a single logarithm. SIMPLIFY!
log4x+log4(x -6)
log4(x2-6x)
300
Find the Greatest Common Factor (GCF) of
315 and 882
What is
63
300
Evaluate the following log.
log5(1/125)
-3
300
Rewrite the following function in exponential form.
log3(1/27)=-3
3-3=(1/27)
300
Solve:
2x^3-1=53
What is x = 3
300
Divide and simplify.
(4x)/(3x-3) -: (x^2+2x)/(x^2+x-2)
4/3
400
Given the functions f(x) x2 and g(x) = x -4
What is g(f(x))? Fully simplify your answer.
g(f(x)) = (x2) - 4
= x2 - 4
400
Completely expand the following logarithms. (Answers have no exponents, multiplication or division)
log54(x)1/3
log54 + (1/3)log5(x)
400
Factor completely
5s^2-16s+12
(5s-6)(s-2)
400
Solve the following equations for x.
log497=x
x = 1/2
400
Log4(1024) = ?
What is 5
400
Solve for x
root4(2x+6)=2
What is
x = 5
400
Simplify
(x^2+8x+12) / (x^2+9x+18)
What is
(x+2)/(x+3)
500
Given f(x) = x2 and g(x) = x - 4
What is f(g(x))? Fully simplify your answer
f(g(x)) = (x - 4)2
=(x -4) (x - 4)
= x2 -4x -4x +16
= x2 -8x +16
500
Completely expand the following logarithms. (Answers have no exponents, multiplication or division)
log(y2/3/3z3x1/5)
(2/3)log(y) -log (3) -3log(z)- (1/5)log (x)
500
Factor Completely
-2c3+8c
-2(c+2)(c-2)
500
Solve the following equations for x.
4x+2=8
x = -1/2
500
Rewrite the following function in exponential form.
103=1000
log1000=3
500
Solve for x
x+3=sqrt(x+5)
What is
x=-1, x=-4
500
Divide and simplify.
(5x^2y^3)/(x^7) div (30xy^4)/(y^3)
y^2/(6x^6)
600
f(x)= 2x/-5. What is f-1(x)?
f-1(x)=-5x/2
600
Use the properties of logarithms to write each of the following as a single logarithm. SIMPLIFY!
log36-4log3y+2log3x
log3(6x2/y4)
600
Solve and identify double roots, if any.
3t^2-10t+3=0
{1/3, 3}
600
Solve the following equation for x. Round to the nearest hundredth if necessary.
logx(6x+27)=2
x = 9
600
Rewrite the following function in the exponential form.
log100(1/10)=-(1/2)
100(-1/2)=(1/10)
600
Solve for x
5sqrt(x-1)=sqrt(x+1)
x = 13/12
600
Divide and simplify.
(3x+27)/(6x-48) div (x^2+9x)/(x^2-4x-32)
(x+4)/(2x)