Exponential Functions
Rewrite in exponential form:
Log 3(2x) = 7
37 = 2x
Convert to Logarithmic form:
Ln (x - 5) = (y + 2)
e(y+2) = (x - 5)
solve:
3x + 4 = 81
x = 0
Solve
log(3x + 3) = log(5x + 1)
x = 1
Exponential and Logarithmic Functions are _______
functions of each other as long as ____________.
inverse
bases are the same
What is the equation of the asymptote for
f(x) = 3x-4 + 2
y = 2
What is the domain and range for
f(x) = log2(x + 3)
domain: (-3, inf)
range: (-inf, inf)
Determine the exact value of x:
4e2x+1 = 12
x = [-1 + ln(3)]/2
Solve
log2(x - 3) = 5
x = 35
What is the meaning of k in this formula:
A = A0(1/2)(t/k)
k = the half life
(the amount of time it takes for A0 to decay to half of A0)
What is the domain and range for
g(x) = (1/2)x+1 + 3
domain: (-inf, inf)
Range: (3, inf)
Simplify: log5(1/125)
-3
Determine the exact solution(s):
e2x - 3ex - 4 = 0
x = ln(4)
Solve:
log3(x) + log3(x - 2) = 1
x = 3
Connecticut has had a zombie outbreak. The outbreak started with 7 zombies, then after 8 days there were 120 zombies. Assuming exponential growth, how many zombies are there after 20 days?
8517.38 parts of zombies makes sense!!
Find the ending amount of an investment of $10000 invested at 4% interest compounded monthly for 5 years.
$12,209.97
Rewrite as a single logarithm:
5 lnx - 4 lny + 2 lnz
ln(x5z2/y4)
Solve for x:
4x-2 = 162x + 1
x = -4/3
Solve
log(4x - 2) - log(2x + 1) = log(5)
What is the property that allows you to solve equations with logarithms on both sides?
If LogaX = LogaY then X = Y
Find the ending investment amount of $32,000 invested at 7% interest compounded continuously for 9 years.
$60083.54
Express and the sum, difference and/or constant multiple of logorithms:
log[(2x+1)3/(5y-2)1/2]
3log(2x+1) - (1/2)log(5y-2)
solve for t: (round to the nearest whole number)
25000 = 5000(1 + .03/4)4t
t = 54 years
solve:
(lnx)2 = lnx
x = e, x = 1
Simplify (no Calculator)
Ln(e4) + Log2(1/64) - Log (0.00001)
3