Rewriting Logs/Exponentials
Log Graphing
Evaluating Logs
Log Properties
Solving Logs
100
What is the inverse of an exponential function?
A LOGARITHMIC FUNCTION (HINT: its the name of the unit)
100
How can we find points on a logarithmic function with only the points from an exponential function?
Switch the x and y values for each coordinate, because exponential functions and logarithmic functions are inverses.
100
Evaluate without a calculator log5(1)
log5(1)=0
100
Is this statement true or false?
log(A)-B=log(A/B)
False, both parts need to have a log in front with the same base.
100
How can we solve for x in this question?
3.5x+2=25
Rewrite as a log and solve for x.
200
Rewrite this exponential function as a logarithmic function.
24=16
log2(16)=4
200
What is the asymptote for the graph
f(x)=3log7(x-4)+3
x=4
Logarithmic functions have vertical asymptotes, so they have equations that are x= (whatever horizontal translation the graph does).
200
Evaluate without a calculator, log(10).
log(10)=1
200
How can we expand the following?
log4(x3)
3log4(x), exponents inside the log can be pulled to the front of the log by using logarithm properties.
200
Solve for x.
log7.8(3x+5)=log7.8(11)
3x+5=11
x=2 (MAKE SURE TO CHECK YOUR ANSWERS)
300
Name all the parts of a logarithmic function (HINT what are the names for a,b, and c in the function below)
loga(b)=c
a=base
b=argument
c=exponent
ac=b is rewritten as an exponential function.
300
Write a function g(x) that transforms the function f(x)=log7(x) such that f(x) is reflected across the x-axis, vertically compressed bafo 1/3, translated right 3, and translated down 7
g(x)=-(1/3)log7(x-3)-7
300
Evaluate without a calculator, log3(81)
log3(81)=4
300
Expand the logarithm, log4(20), choose the correct answers.
A. log4(5)+log4(4) B. log4(5)-log4(4)
C. 4log(20) D. 1+log4(5) E. log4(10)+log4(2)
A,D,E
300
Solve algebraically for x, show your exact answer and approximate answer rounded to the nearest thousandth.
log(2x+12)=2
102=2x+12
x=44
400
Rewrite as a exponential function.
ln(24)=3.178
e3.178=24
400
What does the graph log2x, look like? (Give 2 exact points)
400
Find the value of x, logx(1/64)=-3
x=4
4-3=1/64
400
Use the properties of logarithms to rewrite the expression as a single logarithm.
log5(4)-log5(3)+2log5(2)
log5((4*22)/3)=log5(16/3)
400
Solve for x. Round to the nearest thousandth and show work.
ln(x)+2ln(x2)=5
x=e
500
Rewrite as a logarithmic function.
eb=3c
ln(3c)=b
500
Write the inverse for the function f(x)=6x+3-8
f-1(x)=log6(x+8)-3
500
Evaluate without a calculator, (e2)4ln(e)
e8lne=e8
500
Expand the following, log12((3x5)/y2)
log12(3)+5log12(x)-2log12(y)
500
Devin puts $7000 in an account that earns 5.75% interest compounded continuously. How many years will it take him to reach $20000?
t=(ln(20/7)/0.0575)=18.26 years