Exponentials and Log Quiz

Exponentials

100

Simplify:

\frac{8(a^3)^2}{(2a)^3}

a³

200

Solve for x:

3^{5x-2}=27

1

300

Express as a simple rational number:

2^{3/2}×4^{-1/4}×16^{-3/4}

1/4

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)

500

Solve:

4^{2x+1}>64

x>1

Logarithms

100

Write the following logarithm in exponential form:

log_4(3y)=x

4^x=3y

200

Evaluate the following:

log_2(128)+log_3(45)-log_3(5)

9

300

Solve leaving in exact form:

5^{x-3}=8

log_5(8)+3

400

Simplify:

3/2log_a(a)-log_a(\sqrt{a})

1

500

Solve for x:

log_10(x^2-2x+8)=2log_10(x)

x=4

Graphs

100

What is the asymptote of

f(x)=-3×2^{x-4}-2

y=-3

200

What is the asymptote of

f(x)=4log_2(x-3)+2

x=3

300

Find the x and y intercepts (in exact form) of 

y=-3^x+2

(0,1) and 

(log2/log3,0)

400

Find the x and y intercepts of:

y=log_2(x+2)

(0,1) and (-1,0)

500

Sketch the following being sure to show the asymptote and intercepts.

f(x)=-log_4(x+2)

Mystery

100

Determine the inverse of:

f(x)=3^x+2

f^{-1}(x)=log_3(x-2)

200

Solve:

3^x<5

x<log_3(5)

300

Sketch the following being sure to show the asymptote and intercepts.

f(x)=3^{-x+2}-1

400

Find the domain and range of f(x) given

f^{-1}(x)=log_2(x+2)

Domain: R

Range: (-2,∞)

500

Solve for x:

2^{2x}-6×2^x=-8

x=1 or 2