You're just a bump on a LOG
What is the base of the COMMON logarithm? And what is the base of the NATURAL logarithm? And how do you write it?
Common Log: base 10
Natural Log: base e, "LN"
EXPAND the logarithm using the Law(s) of Logarithms:
\log_7(x^100)
100\log_7(x)
Tell the shifts in the graph, then the equation of the asymptote:
y=log_6 (x-5)-7
Right 5, down 7; x = 5
Solve for x:
\log_6(x)=5
x = 7,776
You invest $150 in an account which has interest compounded continuously at a rate of 4.35%. How long will it take for the account balance to be $1500?
Round your answer to the nearest tenth of a year.
52.9 years
Convert each to the other form (convert between log and exponential form):
log_x 45=7
m^c=8
x^7=45
log_m 8=c
SIMPLIFY the logarithm using the Laws (properties) of Logarithms:
log_7 49^x
2x
What is the first step to graphing a log function (with no shifts)?
What is the next step?
1) Convert to exponential form.
2) Put values (such as -1, 0, 1, 2) in for y and find corresponding x-values.
Solve for x:
log_11(1/(x))=2
x=1/121
A town population grows at an annual rate of 2.5%. In 1995 the population was 12,500. In what year will the population have grown to 85,000?
2072 or 2073
Evaluate the logarithm:
\log_3(81)
4
Simplify the logarithm using the Laws (properties) of Logarithms:
\ln root(3)(e^8)
\8/3
Graph p.23 #8 in your packet/on the whiteboard.
(Teacher will check this one)
Asymptote at x = 1
Domain: x > 1
Range: All Real Numbers
Solve for x:
log_x(4,913)=3
x = 17
A rabbit population grows in such a way that the number of rabbits N after t years is given by the function:
N = 14e^{0.51t}
How many years will it take for there to be 3800 rabbits? Round to the nearest # of years.
11 years
Evaluate the logarithm:
\log(\frac{1}{100})
-2
Given that ln 2 = p and ln 5 = k, write the following in terms of p or k:
ln(1/16)
-4p
Graph p.26 #16 in your packet/whiteboard.
(Teacher will check - graph is shifted up 2)
Asymptote: x = 0
Domain: x > 0
Range: All Real Numbers
Solve for x. Write the exact and approximate answer (rounded to three decimal places).
9^x=18
x=log_9(18)
x=log18/log9
x~~1.315
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.)
18 years
What causes something to be an extraneous solution?
A solution that, when substituted back into the original problem, makes the base or the argument negative.
Given that ln 2 = p and ln 5 = k, write the following in terms of p or k:
ln(125/625)
-k
Graph the following on your whiteboard, then tell the domain, range, and equation of the asymptote:
y=log_3 (x-3)+2
(Teacher will check - graph should be shifted right 3, up 2)
Asymptote: x = 3
Domain: x > 3
Range: All Real Numbers
Solve for x. Be sure to check for extraneous solutions if applicable.
log_3(x^2)=log_3(x+6)
x = 3 or x = -2 (neither is extraneous!)
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