Properties of Logarithms
If there is no base in a logarithm what does it automatically equal?
10
convert bx=a into logarithmic form.
logba=x
what is the first step when solving logarithmic equations?
Condensing the logarithm
Whats the formula for exponential growth?
y(t)=a(1+r)t
logarithmic functions with base "e" are called what?
natural logarithm
In a logarithm subtraction goes with what?
Division
Convert logcx=w to exponential form
cw=x
If the logs on both sides of the equation have the same base then what can you do?
cross them out and solve the arguments like a regular math equation.
Whats the formula for exponential decay?
y(t)=a(1-r)t
what is the value of "e"
2.71828......
In a logarithm adding goes with what?
Multiplication
convert into exponential form: log39=2
32=9
How do you look for extraneous solutions?
1. BEFORE SOLVING: argument has to be greater than 0
(ex. in logba: a>0)
or
2. AFTER SOLVING: check your solution(s)
How would you rewrite this percentage?
3%
two decimal points.
.03
ln24=x
Where should you move the exponent to?
logkmw
the front: wlogkm
convert into logarithmic form:132=168
log13168=2
Solve: log9(6-3w)=log9(-2w)
No Solution
what is the (a) in the following word problem?
Lilly bought a new bike for $150 in 2020. If the bikes value goes down by 15% each year write an exponential function to model the situation.
Note: you do not have to write an equation just find the (a).
$150
condense this expression into a single logarithm:
ln 3+ ln 6
ln(48)
Condense: 2log38=
log382=log364
convert into log form: 83= 6
log86=3
Solve: log468-log44=log4(3n+11)
n=2
Write an exponential growth equation from the following word problem and solve.
In 2021, kenny gained 813 followers on TikTok over a month. If his followers increase by 1.3% each month write an exponential function to find the number of followers he will have in 3 years.
y(3)= 813(1+.013)3
expand this logarithm:
ln 3x
ln 3+ln x