3.4 Exponential and logarithmic Equations and inequalities

Question

Please Provide a video that contains steps on how you were able to get the answer and explain to me so that I can understand

Solve each logarithmic Equations

1.) 3 + log (2x+5) = 2 --------------------> Answer: x = - 49/20

2.) log(x²-x-5) = 0 -----------------------> Answer: x= 3, -2

3.) log₄(x²-7x+14) = 1 ----------------> answer: x = 5, 2

Solve each inequality

1.) 5(0.3)^x + 1 ≤ 11 --------------------> Answer: x ≥ In 2/ In 0.3

2.) -3(1.2)^x + 11 ≥ 8 ----------------------> Anwer: x ≤ 0

3.) Log (5x+15) < 2 ---------------------------> Answer: (-3, 17)

4.) In (x-5) ≥ 1 --------------------------------> Answer: x ≥ e + 5

Answer 1

1.) 3 + log(2x + 5) = 2; 2x + 5 = 0.1; x = -49/10.

3.) log₄(x² - 7x + 14) = 1; x² - 7x + 10 = 0; x = 2 , x = 5

2.) log(x² - x - 5) = 0; x² - x - 6 = 0; x = 3, x = - 2

Inequalities:

1.) 5(0.3)^x + 1 ≤ 11; (0.3)^x ≤ 2; xln(0.3) ≤ ln2; x ≥ ln2/ln(0.3)

2.) -3(1.2)^x + 11 ≥ 8, (1.2)^x ≤ 1; x ≤ 0

3.) Log (5x+15) < 2;0 < 5x + 15 < 100; - 3< x < 17

4.) In (x-5) ≥ 1; x- 5 > e; x > 5 + e