Comparing Log with Exponential
Inverses
What parameter moves the function horizontally? What is something you have to be careful with when dealing with this parameter?
"h" moves the function horizontally. x - h means h units to the right and x + h means h units to the left.
In words what does the following equation mean? (9.1 notes will be helpful)
log_3(81)=4
the exponent you must apply to the base of 3 to get 81is 5
The amount of the radioactive isotope cesium-137 in the environment since 1950 is known. Plants take up cesium-137, which reveals information about when a plant was growing. The function below describes the mass "m" of cesium-137 remaining after "t" years from an initial amount with mass . Write the corresponding equation using the given information: 0.025 microgram of cesium-137 remain from an initial amount of 0.1 microgram?
m=m_0(1/2)^(t/30.1)
0.025=0.1(1/2)^(t/30.1)
Rewrite the exponential equations as a log equations:
e^4=y
4^3=64
ln(y)=4
log_4(64)=3
False. "-a" means to reflect over the x-axis
Convert the equation from exponent to a log equation:
10^-3=1/1000
log(1/1000)=-3
The total population P of the bacteria that turns milk into yogurt can be determined by the function
P(t)=2000(2)^(t/73)
where t is in minutes. How long does it take the population to grow to 64,000 ?
64000=2000(2^(t/73))
32=2^(t/73)
2^5=2^(t/73)
5=t/73
t=365
Given the functions, compare the domain and range:
f(x)=3^x,g(x)=log_3(x)
f(x) domain is all real numbers and range is all numbers greater than 0
g(x) domain is all numbers greater than 0 and range is all real numbers
What transformations have occurred in the following function? (list all of them and be specific!)
f(X)=-2log_6(x-4)+1
reflection over the x axis, vertical stretch by a factor of 2 moved right (horizontally) by 4 and up (vertically) by 1.
2^5=32
The amount of the radioactive isotope cesium-137 in the environment since 1950 is known. Plants take up cesium-137, which reveals information about when a plant was growing. The function below describes the mass "m" of cesium-137 remaining after "t" years from an initial amount with mass . After how long will 0.025 microgram of cesium-137 remain from an initial amount of 0.1 microgram? Round your answer to the nearest tenth if necessary.
m=m_0(1/2)^(t/30.1)
0.025=0.1(1/2)^(t/30.1)
0.25=(1/2)^(t/30.1)
1/4=(1/2)^(t/30.1)
(1/2)^2=(1/2)^(t/30.1)
2=t/30.1
60.2=t
Compare the asymptotes of the functions and give the correct equations:
f(x)=3^x,g(x)=log_3(x)
f(x) has a horizontal asymptote at y = 0 and g(x) has a vertical asymptote at x = 0
Write a logarithmic equation with the following transformations: You may use any base you'd like.
reflection over the x axis, vertical compression by 1/4, left 3 units, up 5 units.
f(x)=-1/4log_b(x+3)+5
f(x)=-1/4ln(x+3)+5
What three buttons do you need to press on the calculator to find the log with a base other than10 or e?
Alpha, Window, 5
The loudness L (in decibels, dB) of a sound is modeled by the function below, where I is the intensity of sound in watts per square meter. What is the loudness in decibels of a subway sound intensity is
10^-3
L=10log(I/10^-12)
90
Which graph will have a y intercept and which graph will have an x intercept? What are the intercepts?
f(x)=3^x,g(x)=log_3(x)
f(x) has a y intercept at (0,1) and g(x) has a n x intercepts at (1,0)
Identify the first two reference points of the following function:
f(X)=-2log_6(x-4)+1
(1+h,k),(b+h,a+k)
(5,1),(10,-1)
Solve for x without a calculator:
log_6(x)=3
6^3=x
36*6=x
216=x
The loudness L (in decibels, dB) of a sound is modeled by the function below, where I is th intensity of sound in watts per square meter. If a jet engine has a loudness of 135 decibels what is its intensity?
L=10log(I/10^-12)
135=10log(I/10^-12)
13.5=log(I/10^-12)
10^13.5=I/(10^-12)
10^(13.5-12)=I
10^1.5=I
31.6=I