You're just a bump on a LOG
What is the word that indicates the COMMON logarithm? And what is its base?
(Hint: it's one of the buttons on your calculator!)
"LOG", base 10
EXPAND the logarithm using the Law(s) of Logarithms:
\log_7(x^100)
100\log_7(x)
This is the equation for what?
A(t)=P(1+\frac{r}{n})^{nt}
Compound Interest
Solve for x:
\log_6(x)=5
x = 7,776
A radioactive mass decays so that at time t (in days) the mass remaining is m(t) kg, and is given by the function:
m(t) = 23e^{-0.0016t}
How many kg was the mass initially?
23 kg
What is the word that indicates the NATURAL logarithm? And what is its base?
(Hint: it's one of the buttons on your calculator!)
"LN", base e
COMBINE the logarithm using the Law(s) of Logarithms:
\ln(q)+\ln(t)+\ln(\pi)
\ln(qt\pi)
;)
What are the corresponding values of n if interest is compounded annually, semiannually, quarterly, monthly, and daily?
Annually: n = 1
Semiannually: n = 2
Quarterly: n = 4
Monthly: n = 12
Daily: n = 365
Solve for x:
log_11(1/(161,051))=x
x = 5
A rabbit population grows in such a way that the number of rabbits n(t) after t years is given by the function:
n(t) = 14e^{0.51t}
How many rabbits are there after 11 years?
3,824 rabbits
Evaluate the logarithm:
\log_3(81)
4
COMBINE the logarithm using the Law(s) of Logarithms:
log_3(x+4)-log_3(x-4)
log_3(\frac{x+4}{x-4})
This is the equation for what?
A(t)=Pe^{rt}
Continuously Compounded Interest
Solve for x:
log_x(4,913)=3
x = 17
An initial bullfrog population of 100 has been growing over the years at a relative growth rate of 40.55%. How many bullfrogs will there be in 14 years?
29,207 bullfrogs
Evaluate the logarithm:
\log(\frac{1}{100})
-2
COMBINE and SIMPLIFY the logarithm using the Law(s) of Logarithms:
ln(x)+ln(x-2)
ln(x^2-2x)
You invest $4,000 at an interest rate of one-eleventh percent, compounded continuously. How much is in your account after 6 years?
$6,901.57
Solve for x:
log_3(\frac{x+4}{x-4})=2
x = 5
An initial bullfrog population of 100 has been growing over the years at a relative growth rate of 40.55%. How many years will it take to reach 45,000 bullfrogs? (round to the nearest whole number.)
15 years
Find the domain of the logarithm:
log_7(x^2-4)
(-\infty, -2) \cup (2, \infty)
EXPAND and SIMPLIFY the logarithm using the Law(s) of Logarithms:
\log_2(\frac{s^3}{4t})
3\log_2(s) - (2+\log_2(t))
\text{or}
3\log_2(s) - 2 - \log_2(t)
You invest $7,600 at an interest rate of 4.5%, compounded daily. How much do you have after 5 years?
$9,517.52
DAILY DOUBLE!
Solve for x:
log_3(x)+log_3(x-6)=3
x = 9
Radium-221 has a half-life of 30 seconds. How long will it take for 64% of a sample to decay?
(round your answer to the nearest whole number.)
44 seconds