Exponentials
Logarithms
Graphs
Mystery
100
Simplify:
\frac{8(a^3)^2}{(2a)^3}
a3
100
Write the following logarithm in exponential form:
log_4(3y)=x
4^x=3y
100
What is the asymptote of
f(x)=-3×2^{x-4}-2
y=-3
100
Determine the inverse of:
f(x)=3^x+2
f^{-1}(x)=log_3(x-2)
200
Solve for x:
3^{5x-2}=27
1
200
Evaluate the following:
log_2(128)+log_3(45)-log_3(5)
9
200
What is the asymptote of
f(x)=4log_2(x-3)+2
x=3
200
Solve:
3^x<5
x<log_3(5)
300
Express as a simple rational number:
2^{3/2}×4^{-1/4}×16^{-3/4}
1/4
300
Solve leaving in exact form:
5^{x-3}=8
log_5(8)+3
300
Find the x and y intercepts (in exact form) of
y=-3^x+2
(0,1) and
(log2/log3,0)
300
Sketch the following being sure to show the asymptote and intercepts.
f(x)=3^{-x+2}-1
400
Simplify into positive index form:
\frac{a^{2n-1}×b^3×c^{1-n}}{a^{n-3}×b^{2-n}×c^{2-2n}}
a^{n+2}b^{n+1}c^(n-1)
400
Simplify:
3/2log_a(a)-log_a(\sqrt{a})
1
400
Find the x and y intercepts of:
y=log_2(x+2)
(0,1) and (-1,0)
400
Find the domain and range of f(x) given
f^{-1}(x)=log_2(x+2)
Domain: R
Range: (-2,∞)
500
Solve:
4^{2x+1}>64
x>1
500
Solve for x:
log_10(x^2-2x+8)=2log_10(x)
x=4
500
Sketch the following being sure to show the asymptote and intercepts.
f(x)=-log_4(x+2)
500
Solve for x:
2^{2x}-6×2^x=-8
x=1 or 2