Exponential Equation and Inequalities

1. Roqui M. Gonzaga,
Lpt
November 10, 2020

2. Prayer

3. Respect (respect everyone in the class)
Effort (show effort and interest)
Attitude (observe your attitude while online class is
ongoing)
Cooperation (cooperate and follow the given
schedule of the task)
Honesty (being honest in doing your offline task will
make you successful)

4. Memo Recall

8. Activity

9. Direction:
Determine whether the following are exponential equation or an exponential
inequalities
1. 3x= 32x−1
2. 2𝑥2 ≥ 32
3. 5x−1= 125
5. 3𝑥2 < 27
4. 2𝑥−2 ≥
1
2
𝑥−3
6. 49 = 7x+1

10. Direction:
Determine whether the following are exponential equation or an exponential
Inequalities.
1. 3x
= 32x−1
2. 2𝑥2 ≥ 32
3. 5x−1= 125
5. 3𝑥2 < 27
4. 2𝑥−2
≥
1
2
𝑥−3
6. 49 = 7x+1
1. Base from the activity, what have you observe?
2. What have you observe from the given symbols?

11. EXPONENTIAL
EQUATION
EXPONENTIAL
INEQUALITIES
Exponential equation are equations
whose exponents are variables.
1. 3x= 32x−1
2. 5x−1= 125
3. 49 = 7x+1
Exponential inequalities are inequalities
with exponents that can be solved
similar to solving traditional equations.
1. 2x2≥ 32
2. 2x−2
≥
1
2
x−3
3. 3x2 < 27

12. EXPONENTIAL EQUATION
 Exponential equation are equations whose exponents are variables.
Example:
1. 3x= 32x−1 2. 5x−1 = 125 3. 49 = 7x+1
To solve:
 Rewrite / express both sides of the equation as powers with the same base.
 If the base is a number, just break it down with a factor tree.
 If the base is a fraction, FIRST write as a whole number by using
negative exponents.
 Solve the resulting equation.

13. EXPONENTIAL EQUATION
 Solve the solution set of the following exponential equation;
1. 2𝑥 = 8
Solution:
2𝑥
= 8
2𝑥 = 23
𝑥 = 3
express both sides of the equation as powers with the same base.
Solve the resulting equation.
Checking:
2𝑥 = 8, since 𝑥 = 3
23 = 8
8 = 8

14. EXPONENTIAL EQUATION
 Solve the solution set of the following exponential equation;
2. 2𝑥
=
1
16
Solution:
2𝑥 =
1
16
2𝑥 =
1
24
2𝑥 = 2−4
𝑥 = −4
express both sides of the equation as powers with the same base.
Since the given base is a fraction, write as a whole number by using
negative exponents.
Checking: 2𝑥 =
1
16
, since 𝑥 = −4
2−4 =
1
16
1
16
=
1
16
Solve the resulting equation.

15.  Solve the solution set of the following exponential equation;
1. 102𝑥 = 0.1 2. 4𝑥+2 = 64 3. 32𝑥−1
+ 5 = 32

16. EXPONENTIAL INEQUALITIES
 Exponential inequalities are inequalities with exponents that can be solved
similar to solving traditional equations.
 Involved inequality symbols.
Example:
1. 2x2≥ 32
2. 2x−2
≥
1
2
x−3
3. 3x2
< 27
Note:
 Inequalities with even number exponents usually
have 2 solution.
 Inequalities with odd exponents contains one
solution.

17. EXPONENTIAL INEQUALITIES
Find the solution set of each of the following exponential inequalities:
1. 2𝑥3 + 14 ≥ 30
Solution:
2𝑥3 + 14 ≥ 30
2𝑥3 + 14 − 14 ≥ 30 − 14
2𝑥3
≥ 16
2𝑥3
2
≥
16
2
𝑥3 ≥ 8
3
𝑥3 ≥
3
8
𝑥 ≥ 2
Apply subtraction property
Solve for x by applying division property
Apply division property
Extract the roots of the expression

18. EXPONENTIAL INEQUALITIES
Find the solution set of each of the following exponential inequalities:
2. 2𝑥2 ≥ 32
Solution:
2𝑥2
≥ 32
2𝑥2
2
≥
32
2
𝑥2
≥ 16
2
𝑥2 ≥
2
16
𝑥 ≥ ±4
Solve for x by applying division property
Apply division property
Extract the roots of the expression
Since the given contains even exponent, then there are 2 solution.
𝑥 ≥ 4 and 𝑥 ≥ −4.

19. Find the solution set of each of the following exponential
inequalities:
1. 3𝑥2 < 27
2. 2𝑥+2 <
1
8

20. Q and A

21. 1. Answer the given problem set.
2. The Assessment of the discussion can be accessed through
sjit.schoology.com.
3. The completion of the lecture ASSESSMENT for each discussion is time-
bounded. You are only given UNTIL MIDNIGHT to complete this. Access
to this activities will automatically be disabled beyond midnight.

22.  Advance study about Logarithmic function, equation
and inequalities.

23. Thank you
and
God bless!