Unit 7

Question 1

Steps to Solving Exponential Equations

Answer 1

1. Use the properties of exponents to simplify each side of the equation
2. Rewrite so both sides have the same base
3. Drop the bases and set the exponents equal to each other

Question 2

Logarithm

Answer 2

Another way of writing exponents

Question 3

Order of Condensing

Answer 3

Power
Product/quotient left to right

Question 4

Order of Expanding

Answer 4

Quotient
Product
Power

Question 5

Steps to log=log

Answer 5

1. Condense each log
2. Use the one to one property
3. Solve and check for extraneous solutions

Question 6

One to One Property

Answer 6

If log base b of m = log base b of n, then m=n

Question 7

Undefined Logs

Answer 7

Negative and zero

Question 8

Steps to log = Number

Answer 8

1. Condense and isolate the log
2. Write the equation in exponential form
3. Solve and check for extraneous solutions

Question 9

Steps to No Common Base

Answer 9

1. Isolate the exponential expression
2. Take the log of both sides
3. May need to expand using power rule
4. Solve and check for extraneous solutions

Question 10

e

Answer 10

Irrational number with an approximate value of 2.718

Question 11

e Occurs In

Answer 11

Base of exponential and log functions that describe real world scenarios

Question 12

Natural Base Exponential Functions

Answer 12

Exponential functions with base e

Question 13

Natural Logs

Answer 13

Log functions with base e

Question 14

f(x) = log base e of x

Answer 14

ln(x)

Question 15

Exponential Growth

Answer 15

Occurs when a quantity exponentially increases over time

Question 16

Exponential Growth Formula

Answer 16

f(t) = a(1+r)^t

Question 17

a=

Answer 17

Intial amount

Question 18

Exponential Decay

Answer 18

Occurs when a quantity exponetially decreases over time

Question 19

Exponential Decay Formula

Answer 19

f(t) = a(1-r)^t

Question 20

Compound Interest

Answer 20

Occurs when interest is calculated on both the principal amount and the accrued interest thus far

Question 21

Compound Interest Formula

Answer 21

A= P(1+(r/n))^n*t

Question 22

b>1

Answer 22

Function is exponential growth and increasing

Question 23

b<1

Answer 23

Fraction
Function is exponential decay and decreasing

Question 24

Asymptote

Answer 24

Vertical determines domain
Horizontal determines range

Question 25

Transformations of Exponential Functions

Answer 25

f(x) = a*b^(x-h)+k

Question 26

Steps to Graphing Exponential Functions

Answer 26

1. a value multiply it to the y value 2. k value add to the new y value 3. h value subtract to x value

Question 27

Raised to Power of Fraction

Answer 27

a^(m/n) = (n√a)^m = (a^m)^(1/n)

Question 28

Roots With Logs

Answer 28

Make it to power of a fraction

Question 29

Compound Interest When FInding t

Answer 29

Isolate log Exponentiate Solve

Question 30

Log Function

Answer 30

Inverse of exponent function

Question 31

Log Graph on Calculator

Answer 31

Use inverse exponential function and then invert the values from the table to the graph using log function

Question 32

Log and Exponential T Tables

Answer 32

Inverses of each other

Question 33

b>1 Looks Like

Answer 33

L upside down

Question 34

0

Answer 34

L

Question 35

Order of Transformations for Log

Answer 35

h, a, and k

Question 36

(a^xb^y)^z=

Answer 36

a^(x*z)b^(y*z)

Question 37

Change Roots To

Answer 37

Exponents Do not bring out