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
Transformations of Exponential Functions
f(x) = a*b^(x-h)+k
Steps to Graphing Exponential Functions
- a value multiply it to the y value
- k value add to the new y value
- h value subtract to x value
Raised to Power of Fraction
a^(m/n) = (n√a)^m = (a^m)^(1/n)
Roots With Logs
Make it to power of a fraction
Compound Interest When FInding t
Isolate log
Exponentiate
Solve
Log Function
Inverse of exponent function
Log Graph on Calculator
Use inverse exponential function and then invert the values from the table to the graph using log function
Log and Exponential T Tables
Inverses of each other
b>1 Looks Like
L upside down
0<b<1 Looks Like
L
Order of Transformations for Log
h, a, and k
(a^xb^y)^z=
a^(xz)b^(yz)
Change Roots To
Exponents
Do not bring out
