Lesson 1.1
What is a logarithm?
The POWER of an exponent!
Evaluate
log_3(243)
5
What does "inverse" means?
Switch x and y
What is the value of "e".
2.718
What is a log equation?
An equation with at least 1 log.
What does "condense" mean?
To make an expression shorter/smaller!
Which log rule is used to solve this problem? You do NOT have to solve.
log_5(x+1) + log_5(4) = 1
product rule
What is my favorite quirk from My Hero Academy?
All for One
What is the base of
log(x)
10
Evaluate
log_7(49) + log_9(729)
5
Is the statement true?
ln(e^2) = e^(ln2
Yes!
A savings account balance is compounded continuously. The interest rate is 3% per year and the current balance is $1,854. What will the balance be 5 years from now? Use
A = Pe^(rt)
$2,154.04
How would you solve the equation below? You do NOT have to solve:
log_2(x-1) = log_2(5x+4)
Cancel out the logs on both sides!
Condense:
log_7(x) - log_7(h)
log_7(x/h)
Which log rule is used to solve this problem? You do NOT have to solve.
ln(x+5) = ln(x-2) - ln(x+6)
quotient rule
How many pets I have?
1
Convert to an exponent
log_2(1024)=10
2^10 = 1024
Which two integers is the log between:
log_4(1/100)
Between -3 and -4
Find the inverse:
h(x) = 1/2 ln(x+9)-4
h^-1(x) = e^(2x+8) -9
Radioactive isotope Berkelium-257 decays exponentially. The continouous decay rate is 50% per thousands of years and the current mass is 804.90 grams. What will the mass be 7 thousand years from now? Use
y = ae^(-kt)
24.31 grams
Solve for x:
2log_3(x+5) = 4
x=4
Expand:
log(5t^2)
log5+2logt
Solve for x:
log(x) + log(7) = log(37)
x = 37/7
How long have I been a teacher in Revere?
11 years.
Convert to a log
e^(x-4) = k
ln(k) = x - 4
Evaluate
4ln(1) * [log_3(3)]
0
Given the function, find its inverse.
f(x) = 5^(x+3)
f^-1(x) = log_5(x)-3
The initial population of a colony of bacteria in a petri dish is 1500. The colony grows at a rate of 5.7% per hour. The next observed population of the colony of bacteria was 2800. How many hours passed between observations?
Use
y = ae^(kt)
t ~~ 10.95 or 11
Solve for t:
ln(t+1)=ln(4-2t)
t=1
Condense:
1/2[ln(x) + ln(3)]
ln(3x)^(1/2)
Solve for t:
log_9(t + 6) - log_9(t) = 1
t= 3/4
Will we have alot of HW?
YES
Convert to an exponent
log_(1/x)(15-y) = 13cd
(1/x)^(13cd) = 15-y
Evaluate
log_125(25)
2/3
Given the function, evaluate the inverse:
v(x) = log(x^2 + 16x + 64)
y = -8+- sqrt(10^x)
A radioactive isotope decays continuously from an initial quantity of 12,000 to 1,600 over the course of 8 days. What is the decay rate (per day) of the isotope as a percentage?
k ~~ -0.25186
Solve for x:
log(x^2 - 16) = log(-6x)
x = -8
Expand:
ln((3x^2)/z)
ln(3) + 2ln(x) - lnz
Solve for x
ln(x-3) - ln(x-5) = ln(5)
x = 11/2
What is my favorite grade to teach?
11-12 grade! I can't pick a favorite...I'm sorry...