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Solving Rational, Exponential, Logarithmic Equations, Study notes of Mathematics

Mathematics

Solving Rational, Exponential, Logarithmic Equations

Typology: Study notes

2020/2021

Uploaded on 10/01/2021

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St. Rose Catholic School, Inc.
Paniqui, Tarlac
GENERAL MATHEMATICS
SOLVING RATIONAL, EXPONENTIAL, AND LOGARITHMIC
EQUATIONS
NAME:
YEAR AND SECTION:
DATE:
RATIONAL EQUATION
Solve for x of the following rational equations. Show your complete solutions.
(3points each)
1. 2
๐‘ฅ+2 +3
๐‘ฅ=โˆ’๐‘ฅ
๐‘ฅ+2
2. 7๐‘ฅ
3๐‘ฅ+3 โˆ’5
4๐‘ฅโˆ’4 =3๐‘ฅ
2๐‘ฅ+2
3. 1
๐‘ฅ=๐‘ฅโˆ’34
2๐‘ฅ2
4. 1
๐‘ฅ=6
5๐‘ฅ + 1
5. 12
๐‘ฅ+ (๐‘ฅ โˆ’ 8) = 0
EXPONENTIAL EQUATION
Solve for x of the following exponential equations. Show your complete solutions.
(3points each)
1. 362๐‘ฅ+3 = ( 1
216)โˆ’2๐‘ฅ
2. 64โˆ’๐‘ฅโˆ’1 =16
3. (1
125)2๐‘ฅโˆ’2 =125
4. 7๐‘ฅ+4 =492๐‘ฅโˆ’1
5. 125๐‘ฅโˆ’1 =25๐‘ฅ+3
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St. Rose Catholic School, Inc.

Paniqui, Tarlac

GENERAL MATHEMATICS

SOLVING RATIONAL, EXPONENTIAL, AND LOGARITHMIC

EQUATIONS

NAME:

YEAR AND SECTION:

DATE:

RATIONAL EQUATION

Solve for x of the following rational equations. Show your complete solutions. (3points each)

2 ๐‘ฅ+2 +^

3 ๐‘ฅ =^

โˆ’๐‘ฅ ๐‘ฅ+

2. 3๐‘ฅ+37๐‘ฅ โˆ’ 4๐‘ฅโˆ’4^5 = 2๐‘ฅ+23๐‘ฅ

1 ๐‘ฅ =^

๐‘ฅโˆ’ 2๐‘ฅ^2

1 ๐‘ฅ =^

6 5๐‘ฅ + 1

12 ๐‘ฅ + (๐‘ฅ โˆ’ 8) = 0

EXPONENTIAL EQUATION

Solve for x of the following exponential equations. Show your complete solutions. (3points each)

1. 36 2๐‘ฅ+3^ = (

1 216 )

โˆ’2๐‘ฅ

2. 64 โˆ’๐‘ฅโˆ’1^ = 16

1 125 )

2๐‘ฅโˆ’ = 125

4. 7 ๐‘ฅ+4^ = 492๐‘ฅโˆ’

5. 125 ๐‘ฅโˆ’1^ = 25๐‘ฅ+

LOGARITHMIC EQUATION

Solve for x of the following logarithmic equations. Show your complete solutions. (3points each)

  1. log ๐‘ฅ โˆ’ log 5 = log 2 โˆ’ log(๐‘ฅ โˆ’ 3)
  2. log(6๐‘ฅ + 5) โˆ’ log 3 = log 2 โˆ’ log ๐‘ฅ
  3. log 3 (20) โˆ’ ๐‘ฅ + 2 = 4
  4. log 8 (๐‘ฅ + 16) + log 8 (๐‘ฅ + 14) = 2
  5. log 2 (2๐‘ฅ + 3) + log 2 (๐‘ฅ + 1) โˆ’ log 2 (๐‘ฅ โˆ’ 3) = 3