Properties of Logarithms
If there is no base in a logarithm what does it automatically equal?
10
what is the equation for logarithmic form?
logba=x
what is the first step when solving logarithmic equations?
Condensing the logarithm
Whats the formula for exponential growth?
f(t)=a(1+r)t
logarithmic functions with base "e" are called what?
natural logarithm
In a logarithm subtraction goes with what?
Division
what is the formula for exponential form?
bx=a
If two logs have the same base then what can you do?
cross them out and solve like a regular math equations.
f(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
At the end when checking your answer what can NOT be in the logarithmic equation?
A negative
How many decaml points must you move over in order to have the correct (b)?
How would you rewrite this percentage?
3%
two decimal points.
.03
ln24=x
Where should you move the exponent too?
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 a year.
f(12)= 813(1+.013)12
expand this logarithm:
ln 3x
ln 3+ln x