Logarithms
Expand
log((3\sqrtx)/y^3)
log3+1/2 logx-3logy
Solve
2^(3x-6)=8^(-2x+1)
x=1
Simplify the equation and express the domain in interval notation
f(x)=(2x+6)/(x^2-x-12)
f(x)=2/(x-4)
D=(-\infty,-3)\cup(-3,4)\cup(4,\infty)
Factor completely the expression knowing that 2 is a zero of the function
f(x)=x^5 - x^4 - 2 x^3 - x^2 + x + 2
f(x)=(x+1)(x-1)(x^2+x+1)
Condense 2logx-1/2logy-3logz
log(x^2/(z^3\sqrty))
Solve
9^(-2x+1)=(1/27)^(x+5)
x=17
The graph of f has a hole. Give its coordinates.
f(x)=(x^2-x-2)/(x^3+x^2-3x-3)
(-1, 3/2)
Find (f\circg)(x) and its domain
f(x)=x^2, g(x)=\sqrt(2-x)
(f\circ g)(x)=2-x, D=(-\infty, 2]
Solve. Identify any extraneous solution.
log_9(x-1)-log_9(x+5)=1/2
No solution. -8 is extraneous
Find the inverse of
f(x)=5-3^{2x-1}
f^(-1)(x)=(log_3(5-x)+1)/2
What is the equation of the horizontal asymptote of f ?
f(x)=(2x^3-4x^5+3)/(2x^5+x-6)
y=-2
Solve
|x^2+5x|=6
{-6, -3, -2, 1}
What are the x- and y-intercepts of the graph of f, if they exist.
f(x)=log_5(x-3)-2
No y-intercept. the x-intercept is
28
You invest $1000 in an account that serves 2.4% interest compounded monthly.
How much do you have on the account after 16 months?
Use P=A(1+r/n)^(nt)
and round to the nearest penny
$ 1032.48
Solve the inequality
(x-1)/(x+3)<=5
(-\infty, -4]\cup(-3,\infty)
What is the absolute minimum of f ?
f(x)=2x^2-4x+5
3
Find the domain of f
f(x)=5log_5(x^2-9)+7
(-\infty, -3)\cup(3, \infty)
Radon-222 has a half-life of about 3.8 days.
What is its decay rate to the nearest hundredth
Use A=Pe^(rt)
r=0.18
What is the equation of the slant asymptote of f ?
f(x)=(2x^3-3x^2+6)/(3x^2-5)
y=2/3 x-1
Solve the system
x^2+xy=5
x-y=9
{(5,4), (-1/2, -19/2)}