gen math

Question 1

The inverse of the exponential function is
called

Answer 1

logarithmic function

Question 2

Write each Exponential Equation in
Logarithmic Form.

81 = 3𝑥 means
10 0.01 2 means
𝑒ʸ = 9 means

Answer 2

log 81= x
og10 0.01 = -2
loge 9=y

Question 3

log^2 64 = 6

Answer 3

𝟐⁶ = 𝟔4

Question 4

log a M =7

Answer 4

𝒂⁷ = m

Question 5

are logarithms with
base 10; 𝒍𝒐𝒈𝒙 is a short notation for
𝒍𝒐𝒈𝟏𝟎^X

Answer 5

Common Function

Question 6

An equation involving logarithms
Example
𝒍𝒐𝒈𝒙𝟐 = 4

Answer 6

Logarithmic Equation

Question 7

are logarithms to the
base 𝒆 (approximately 2.71828), and
are denoted by “𝒍𝒏”
In other words, 𝒍𝒏 𝒙 is another way of
writing 𝒍𝒐𝒈𝒆
𝒙.

Answer 7

Natural logarithms

Question 7

An inequality involving logarithms
Example
𝒍𝒏 𝒙𝟐 > 𝒍𝒏 𝒙�

Answer 7

Logarithmic Inequality

Question 8

Function of the form 𝒇(𝒙) = 𝒍𝒐𝒈𝒃𝒙(𝒃 > 𝟎, 𝒃 ≠ 𝟏)
Example
𝒈 𝒙 = 𝒍𝒐𝒈𝟑�

Answer 8

Logarithmic Function

Question 9

Solving logarithmic equations
b. 𝒍𝒐𝒈𝟓𝟔𝒙 = 𝒍𝒐𝒈𝟓^24

Answer 9

Solution.
𝒍𝒐𝒈𝟓𝟔𝒙 = 𝒍𝒐𝒈𝟓𝟐𝟒
𝟔𝒙 = 𝟐𝟒
𝟔𝒙=24
𝟔x=𝟐𝟒
𝟔 6
𝒙 = 4

Question 9

b. 𝒍𝒐𝒈𝟑𝒙 ≤ 5

Answer 9

𝒍𝒐𝒈𝟑𝒙 ≤ 𝟓
𝒙 ≤ 𝟑^𝟓
𝒙 ≤ 𝟐𝟒𝟑
𝟎 < 𝒙 ≤ 𝟐𝟒𝟑
𝒐𝒓
(𝟎, 𝟐𝟒3)

Question 9

Solving logarithmic equations
a. 𝒍𝒐𝒈𝟓𝒙 = 4

Answer 9

Solution.
𝒍𝒐𝒈𝟓𝒙 = 𝟒
𝒙 = 𝟓^4
𝒙 = 𝟔𝟐5

Question 9

❑ Annually

Answer 9

1

Question 9

Property of Logarithmic
Inequalities

. 𝒍𝒐𝒈𝟒𝒙 ≥ 3

Answer 9

Solution.
𝒍𝒐𝒈𝟒𝒙 ≥ 𝟑
𝒙 ≥ 𝟒^𝟑
𝒙 ≥ 𝟔4

Question 10

❑ Monthly

Answer 10

12

Question 10

is the interest on savings calculated on both the initial
principal and the accumulated
interest from previous periods.

Answer 10

Compound Interest

Question 10

compound interest formula

Answer 10

A=P(1+r/n)^nt

Question 10

In general, when interest is compounded annually
for 𝒏 years, the amount (or future value) 𝐀 is

Answer 10

𝐀 = 𝐏 𝟏 + 𝐫^t

Question 10

❑ Semi Annually

Answer 10

2

Question 10

❑ Quarterly

Answer 10

4

Question 10

person (or institution) who
owes the money or avails of the funds from the
lender

Answer 10

Borrower
or debtor

Question 10

person (or institution) who
invests the money or makes the funds available

Answer 10

Lender or creditor

Question 10

the interest

Answer 10

𝐈 = 𝐀 − P

Question 11

date on which money is
received by the borrower

Answer 11

Origin
or loan date

Question 11

amount of time in years
the money is borrowed or invested

Answer 11

Time or term (𝒕)

Question 11

annual rate, usually in percent,
charged by the lender, or rate of increase of
the investment

Answer 11

Rate
(𝒓)

Question 11

a date on which
the money borrowed or loan is to be completely
repaid

Answer 11

Repayment
date or maturity date

Question 11

amount paid or earned for the
use of money

Answer 11

Interest
(𝑰)

Question 11

amount of money borrowed
or invested on the origin date

Answer 11

Principal (𝑷)

Question 12

is charged only on the loan
amount called the principal.

Answer 12

Simple interest

Question 12

find I

Answer 12

I=PRT

Question 12

find P

Answer 12

P=I/rt

Question 12

find r

Answer 12

R=i/pt

Question 12

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.

Answer 12

Maturity Value (or future value)

Question 12

find t

Answer 12

t=i/pr

Question 13

Maturity Value or (Amount or
Balance) Formula

Answer 13

A=𝐏+I

Question 13

face value or the
present value of the loan.

Answer 13

Principal P

Question 13

– interest based on a 360-day year.

Answer 13

Ordinary Interest or Banker’s Interest

Question 13

– interest based on a 365-day year.

Answer 13

Exact Interest