Exact Value
Exponential Equations
Log Equations
Condense & Expand
Graphs
100
What is the exact value of:
ln e
1
100
Solve for x:
4^-x = 64
x = -3
100
Solve for x:
log_3 x = 2
x = 9
100
Expand and simplify completely:
log_3 (x^2y^4)
2log_3x + 4log_3y
100
What is the relationship of the functions below? Explain.
f(x) = 3^x + 2
g(x) = log_3 (x - 2)
f(x) and g(x) are inverses; their x & y values swap, their vertical and horizontal asymptotes swap, their domain and ranges swap
200
What is the exact value of:
log_(1/2) 8
-3
200
Solve for x:
e^x = e^(3x+8)
x = -4
200
Solve for x:
log_x 64 = 2
x = 8
200
Condense and simplify completely:
5log_7(x) + 4log_7(y)
log_7(x^5y^4)
200
f(x) = 3^x
1. Graph and label: 3 key points, horizontal asymptote, and both axes completely.
2. Find domain and range.
x in (-\infty,\infty)
y in (0, \infty)
300
What is the exact value of:
log sqrt10
1/2
300
Solve for x:
9^(x^2) = 27^x
x = 0, 3/2
300
Solve for x:
ln e^(3x) = 12
x = 4
300
Expand and simplify completely:
ln(e/x^2)
1-2lnx
300
f(x) = log_3 (x)
1. Graph and label: 3 key points, vertical asymptote, and both axes completely.
2. Find domain and range.
x in (0, \infty)
y in (-\infty, \infty)
400
What is the exact value of:
5^(log_5 7)
7
400
Solve for x:
5^(x^2+8) = 125^(2x)
x = 2, 4
400
Solve for x:
log_5 (x^2) = 2
x = -5, 5
400
Condense and simplify completely:
4log_2(sqrtx) - 5log_2(y)
log_2((x^2)/(y^5))
400
f(x) = 4^x - 1
1. Graph and label: 3 key points, horizontal asymptote, and both axes completely.
2. Find domain and range.
x in (-\infty, \infty)
y in (-1, \infty)
500
What is the exact value of:
3^(log_3 4 - log_3 2)
2
500
Solve for x:
4^x*2^(x^2) = 16^2
x = -4, 2
500
Solve for x:
log_3 (x^2 + 1) = 2
x = -2sqrt2, 2sqrt2
500
Condense and simplify completely:
log(x^2+3x+2) - 2log(x+1)
log((x+2)/(x+1))
500
f(x) = log_4 (x+1)
1. Graph and label: 3 key points, vertical asymptote, and both axes completely.
2. Find domain and range.
x in (-1, \infty)
y in (-\infty, \infty)