Unit 7 Flashcards
Steps to Solving Exponential Equations
- Use the properties of exponents to simplify each side of the equation
- Rewrite so both sides have the same base
- Drop the bases and set the exponents equal to each other
Logarithm
Another way of writing exponents
Order of Condensing
Power
Product/quotient left to right
Order of Expanding
Quotient
Product
Power
Steps to log=log
- Condense each log
- Use the one to one property
- Solve and check for extraneous solutions
One to One Property
If log base b of m = log base b of n, then m=n
Undefined Logs
Negative and zero
Steps to log = Number
- Condense and isolate the log
- Write the equation in exponential form
- Solve and check for extraneous solutions
Steps to No Common Base
- Isolate the exponential expression
- Take the log of both sides
- May need to expand using power rule
- Solve and check for extraneous solutions
e
Irrational number with an approximate value of 2.718
e Occurs In
Base of exponential and log functions that describe real world scenarios
Natural Base Exponential Functions
Exponential functions with base e
Natural Logs
Log functions with base e
f(x) = log base e of x
ln(x)
Exponential Growth
Occurs when a quantity exponentially increases over time
Exponential Growth Formula
f(t) = a(1+r)^t
a=
Intial amount
Exponential Decay
Occurs when a quantity exponetially decreases over time
Exponential Decay Formula
f(t) = a(1-r)^t
Compound Interest
Occurs when interest is calculated on both the principal amount and the accrued interest thus far
Compound Interest Formula
A= P(1+(r/n))^n*t
b>1
Function is exponential growth and increasing
b<1
Fraction
Function is exponential decay and decreasing
Asymptote
Vertical determines domain
Horizontal determines range
