gen math Flashcards
exam Q2
The inverse of the exponential function is
called
logarithmic function
Write each Exponential Equation in
Logarithmic Form.
81 = 3π₯ means
10 0.01 2 means
πΚΈ = 9 means
log 81= x
og10 0.01 = -2
loge 9=y
log^2 64 = 6
πβΆ = π4
log a M =7
πβ· = m
are logarithms with
base 10; ππππ is a short notation for
πππππ^X
Common Function
An equation involving logarithms
Example
πππππ = 4
Logarithmic Equation
are logarithms to the
base π (approximately 2.71828), and
are denoted by βππβ
In other words, ππ π is another way of
writing ππππ
π.
Natural logarithms
An inequality involving logarithms
Example
ππ ππ > ππ ποΏ½
Logarithmic Inequality
Function of the form π(π) = πππππ(π > π, π β π)
Example
π π = πππποΏ½
Logarithmic Function
Solving logarithmic equations
b. ππππππ = ππππ^24
Solution.
ππππππ = ππππππ
ππ = ππ
ππ=24
πx=ππ
π 6
π = 4
b. πππππ β€ 5
πππππ β€ π
π β€ π^π
π β€ πππ
π < π β€ πππ
ππ
(π, ππ3)
Solving logarithmic equations
a. πππππ = 4
Solution.
πππππ = π
π = π^4
π = ππ5
β Annually
1
Property of Logarithmic
Inequalities
. πππππ β₯ 3
Solution.
πππππ β₯ π
π β₯ π^π
π β₯ π4
β Monthly
12
is the interest on savings calculated on both the initial
principal and the accumulated
interest from previous periods.
Compound Interest
compound interest formula
A=P(1+r/n)^nt
In general, when interest is compounded annually
for π years, the amount (or future value) π is
π = π π + π«^t
β Semi Annually
2
β Quarterly
4
person (or institution) who
owes the money or avails of the funds from the
lender
Borrower
or debtor
person (or institution) who
invests the money or makes the funds available
Lender or creditor
the interest
π = π β P
date on which money is
received by the borrower
Origin
or loan date
amount of time in years
the money is borrowed or invested
Time or term (π)
annual rate, usually in percent,
charged by the lender, or rate of increase of
the investment
Rate
(π)
a date on which
the money borrowed or loan is to be completely
repaid
Repayment
date or maturity date
amount paid or earned for the
use of money
Interest
(π°)
amount of money borrowed
or invested on the origin date
Principal (π·)
is charged only on the loan
amount called the principal.
Simple interest
find I
I=PRT
find P
P=I/rt
find r
R=i/pt
the amount to be paid on the due
date of a loan or the amount to be paid
to an investor at the end of the period
for which an investment has been
made.
Maturity Value (or future value)
find t
t=i/pr
Maturity Value or (Amount or
Balance) Formula
A=π+I
face value or the
present value of the loan.
Principal P
β interest based on a 360-day year.
Ordinary Interest or Bankerβs Interest
β interest based on a 365-day year.
Exact Interest
