To _______ an equation for x means to find all values of x for which the equation is true.
Solve/Evaluate
100
Solve for x.
4^x = 16
x = 2
100
Solve for x algebraically.
e^x = e^(x^2 - 2)
x = -1 and 2
100
Solve for x algebraically. Then, approximate your answer to three decimal places.
ln x = -3
x = .050
100
$2500 is invested in an account at an interest rate of 5%, compounded continuously. Find the time required for the amount to double. Solve for t both algebraically and approximate to three decimal places.
t = 13.863 years
200
a^x = a^y, if and only if _________.
x = y
200
Solve for x.
ln x - ln 2 = 0
x = 2
200
Solve for x algebraically.
e^(-x^2) = e^(x^2 - 2x)
x = 0 and 1
200
Solve for x algebraically. Then, approximate your answer to three decimal places.
ln x - 7 = 0
x = 1096.633
200
$2500 is invested in an account at an interest rate of 3.75%, compounded continuously. Find the time required for the amount to triple. Solve for t both algebraically and approximate to three decimal places.
t = 29.296 years
300
log base a of x = log base a of y if and only if __________.
x = y
300
Solve for x.
(1/4)^x = 64
x = -3
300
Solve for x algebraically. Then, approximate the result to three decimal places.
4(3^x) = 20
x = 1.465
300
Solve for x algebraically. Then, approximate your answer to three decimal places.
3 ln 5x = 10
x = 5.606
300
The demand for a limited edition coin set is
p = 1000 [1 - 5/(5 + e^-0.001x)]. Find the demand x for a price of $139.50.
x = 210 coins
400
Log base a of a^x = ___________.
x
400
Solve for x.
e^x = 2
x = ln 2 (approximately 0.639)
400
Solve for x algebraically. Then, approximate your answer to three decimal places.
e^x - 9 = 19
x = 3.332
400
Solve for x algebraically. Then, approximate your answer to three decimal places.
2 - 6 ln x = 10
x = 0.435
400
The demand for a limited edition coin set is
p = 1000 [1 - 5/(5 + e^-0.001x)]. Find the demand x for a price of $99.99.
x = 588 coins
500
a^(log base a of x) = ____________.
x
500
Solve for x.
Log base 5 of x = 1/2
x = 5^(1/2) which is approximately 2.236
500
Solve for x algebraically. Then, approximate your answer to three decimal places.
2^(3-x) = 565
x = -6.142
500
Solve for x algebraically. Then, approximate your answer to three decimal places.
ln x - ln (x + 1) = 2
No Solution
500
The yield v (in millions of cubic feet per acre) for a forest at age t years is given by v = 6.7e^(-48.1/t). Find the time necessary to obtain a yield of 1.3 million cubic feet.