5A
log2(1/64) = x
x = -6
Write as a single logarithm:
2log6(x) - 4log6(y)
log6(x2/y4)
Solve the equation:
44x+1 = 8x-4
x = -14/5
4(10)n = 4000
n = 3
Find the time it takes for $5400 to double when invested at an annual interest rate of 3%, compounded continuously. Round the answer to the nearest tenth.
23.1 years
log1234567890(1)
0
Given ln(a) = -2, ln(b) = 3, and ln(c) = 5, evaluate the following:
a) ln(a/b5c3)
b) (ln(c-3))(ln(a5/b3))
a) -32
b) 285
Solve the equation:
(2)-x/12 = 7
-12log2(7)
Solve the equation:
24 - 60e-3w+1 = -1401
(ln(23.75) - 1) / (-3)
The number of bacteria in a culture is given by the function, n(t)=960e0.4t, where t is measured in hours.
a) What is the relative rate of growth of this bacterium population?
b) What is the initial population of the culture?
c) How many bacteria will the culture contain at time t=5? Round to the nearest whole bacteria.
a) 40%
b) 960 bacteria
c) 7093 bacteria
loga(an)
3
Write as a sum and/or difference of logarithms. Express powers as coefficients.
log2(32/(x-1)1/2)
5 - (1/2)log2(x-1)
2ex - 20 = 9
a) Exact answer
b) Answer rounded to 4 decimal places
a) ln(29/2)
b) 2.6741
23x + 23x+1 = 24
x = 1
You deposit $2000 in an account earning 7% interest compounded monthly. How much will you have in the account in 10 years?
$4019.32
ln(ex) = z
z = x
Write as a single logarithm.
5 - ln(x)
ln(e5/x)
e2x - ex - 6 = 0
x = ln3
2(6x+1 + 3) = 202
(ln98)/(ln6) - 1
Students in a fifth-grade class were given an exam. During the next 2 years, the same students were retested several times. The average score was given by the model:
f(t) = 91 - 8log(t+1), 0 <= t <= 24
where t is the time in months. Round all answers to the nearest tenth.
a) What is the average score on the original exam?
b) What was the average score after 6 months?
c) What was the average score after 18 months?
a) 91
b) 84.2
c) 80.8
Find the domain of the function:
y = log(8+2x)
(-4, oo)
Write as a single logarithm.
2lnx + 9lny - 2(lnz + 8lnw)
ln((x2y9)/(z2w16))
107x-7 = 65x-9
(7ln10 - 9ln6) / (7ln10 - 5ln6)
Solve the equation. Determine if the solution(s) are extraneous.
log2(z) + log2(z+13) = log2(16)
z = (-13 + sqrt233) / (2) ; not extraneous
z = (-13 - sqrt233) / (2) ; extraneous
An unknown radioactive element decays into non-radioactive substances. In 780 days the radioactivity of a sample decreases by 64 percent.
a) Find the decay constant k. (Round your answer to 5 decimal places.)
b) What is the half-life of the element? (Round your answer to two decimal places)
c) How long will it take for a sample of 100 mg to decay to 86 mg? (Round your answer to two decimal places)
a) k = -0.00131
b) 529.12 days
c) 115.13 days