Simplifying Logarithmic Expressions
Evaluate.
log_64(2)
1/6
Solve. Give an exact answer.
7(4)^(x - 3) = 13
log_4(13/7) + 3
Solve.
log_11(-5x) = log_11(-x + 8)
-2
What is the domain and range of
y = -2^(x) - 2
Domain:
(-oo, oo)
Range:
(-oo, -2)
What is the domain and range of the following function.
y = log(x + 4) - 2
Domain:
(-4, oo)
Range:
(-oo, oo)
Evaluate.
e^ln6
6
Solve. Give an exact answer.
8(20)^(x - 2) + 2 = 71
log_20(69/8) + 2
Solve.
log_3(10x + 3) = log_3(x^2 + 12)
x = 1, 9
What are the x and y intercepts of the function
y = -e^(2x) + 3
(ln3/2, 0), (0, 2)
What are the x and y intercepts of the following function?
y = log_4(x + 2) - 5
(0, -9/2), (1022, 0)
log_9(27)
3/2
Solve. Give an exact answer.
-3^(4x-5) - 8 = -41
(log_3(33) + 5)/4
Solve.
-3log_7(-8x - 4) - 4 = -7
x = -11/8
What is the end behavior of the function
y = (1/2)^x + 1
x -> oo, f(x) -> 1
x -> -oo, f(x) -> oo
Describe the end behavior of the following function.
y = log_(1/4)(x - 1) + 8
x -> oo, f(x) -> -oo
x-> 1^+, f(x) -> oo
If
ln(2) = 0.693
ln(3) = 1.099
Find
ln(18)
2.891
Solve. Give an exact answer.
4(10)^(-8x - 1) - 2 = 90
(-log23 - 1)/8
Solve. Give an exact, simplified answer.
log_5(7 - 2x^2) + log_5(10) = log_5(60)
x = +-sqrt2/2
Consider the function:
y = 2(1/2)^(3x + 1) - 5
Transform these three coordinates from the parent function.
(-1, 2), (0, 1), (1, 1/2)
(-2/3, -1), (-1/3, -3), (0, -4)
For the function
y = 3log_(1/2)(-2x + 3) - 7
transforms these coordinates from the parent function:
(1/2, 1), (1, 0), (2, -1)
(5/4, -4), (1, -7), (1/2, -10)
If
log3 = 0.477, log4 = 0.602, log6 = 0.778
Find
log(8)
0.903
Solve. Give an exact answer.
-5e^(3x - 9) + 3 = -6
(ln(9/5) + 9)/3
Solve. Give an exact answer.
ln9 - ln(2-4x) = 1
x = (-9+2e)/(4e)
Consider the function:
y = -e^(-2x + 4) + 3
Transform the coordinates from the parent function for x = 0, 1, and 2. Write the asymptote equation, domain, range, and x/y intercepts. All answers should be exact!
Coordinates:
(2, 2), (3/2, -e+ 3), (1, -e^2 + 3)
Asymptote:
y = 3
Domain:
(-oo, oo)
Range:
(-oo, 3)
Intercepts:
(0, -e^4 + 3) ((ln3 - 4)/-2, 0)
For the function
y = 1/2ln(4x - 8) + 2
Transform these coordinates from the parent function for x = 1, e, and e^2. Then write the asymptote equation, domain, range, and x/y intercepts.
Coordinates:
(9/4, 2), (e/4 + 2, 5/2), (e^2/4 + 2, 3)
Asymptote:
x = 2
Domain:
(2, oo)
Range:
(-oo, oo)
Intercepts: no y-intercept
(1/(4e^4) + 2, 0)