Natural Logarithms
Word Problems
Logarithms
Exponential Equations
Graphing
100
Evaluate: - ln 1
0
100
One isotope of chromium has a half-life of 23 hours. How long does it take 50 g to decay to 40 g?
7.4 hours
100
Evaluate log28√(2)
7/2
100
Solve: 27x+1 = 81
1/3
100
Graph and find domain and range
f(x)=5*(1/2)^(x-2) -1
Domain: all real numbers
Range: y>-1
200
Evaluate: ln (1/(3√(e^2)))
-2/3
200
How much will a $4000 investment be worth after 5 years if it is invested at 8% interest compounded quarterly?
$5943.79
200
Solve: log8x = -1/3
1/2
200
Solve: (1/10)y = 100y+3
-2
200
Graph and find domain and range.
f(x) = 4*2^(x+1) -2
Domain: all real numbers
Range: y>-2
300
Evaluate:
e^{\ln e^3}
e^3
300
How long does it take an investment to double in value if it is invested at 12 % compounded monthly?
5 years 10 months
300
Express in terms of log4A and log4B: log4(A2/√(B))
2 log4A - 1/2 log4B
300
Solve:
36\sqrt{6} = 6^{2x+1}
3/4
300
Describe how the graph of
g(x) = -\frac{1}{2}*3^{x+1}+4
is related to the graph of
f(x) =3^x
It is reflected horizontally, vertically compressed, translated left 1 unit and up 4 units.
400
Solve: ln x + ln 3 = ln (x+4)
x = 2
400
The population of a certain type of bacteria doubles every 10 hours. How long will it take the population to triple?
15.8 hours
400
Solve: logax + loga(2x+3) = loga2
1/2
400
(sqrt{\frac{1}{27}})^{x+1} = 9^{x-1}
1/7
400
Each year, the number of pay phones in millions decreases by 10%. The number of pay phones in 1999 was 2.9 million. Graph the function modeling the the number of pay phones from 1999 to 2009.
500
Condense:
ln 4 - 3 - ln2
ln(\frac{2}{e^3})
500
Jonathan wants to have $5000 in 4 years. It is compounded continuously at a rate of 4%. How much does he need to invest?
$4,260.72
500
Condense into one logarithm:
1-3log_5 x
log_5frac{5}{x^3}
500
Solve: 5x - 6x =0
0
600
Solve: 3e2x + 2 = 50
x = ln 4
600
A colony of bacteria has 6.5 x 106 members at 8AM and 9.75 x 106 members at 10:30AM. Find its population at noon.
1.24 x 107 members
600
Solve: log3(x+2) + log36 = 3
5/2
700
3e2x -12ex+ 12 = 0
x = ln 2