Solve the exponential equation. When approximating, give answers to five decimal

Question

Solve the exponential equation. When approximating, give answers to five decimal places of accuracy. You may wish to check your solution graphically. 2^x = 16 3^-x = 1/9 25^3x = 125^x + 1 3^x^2 + 1 = 27 7^x = 10 5^x = 10 3^-x = 11 3^x - 1 = 2^x (3/5)^x = 6^2 - x 0.4^2 + x = 1.5^3x - 1 e^x = 2^x + 1 5e^-2.3x = 4 e^2x - 1 = pi^2x e^x/2 = 3^x/4 1/2^x + 2 = 1/8 (2/3)^-x + 1 = 81/16 1.06^t = 1000 1000 e^0.05 t = 2000 Approximate the solution(s) of the equation to the nearest hundredth. 4^x - 3 middot 2^x + 2 = 0 e^-x = x 4 - x^2 = e^x- 2 1/25 x^4 + 4 = x^2 + e^x + 1 1/8x^3 + 7/8x^2 = x + 2 - e^x

Explanation / Answer

11. 2^x = 16

2^x = 2^4

x = 4

13 . 25^3x = 125^(x+1)

5^6x = 5^(3x+3)

6x = 3x +3 ; x = 1

15.   7^x = 10

Take natural log on both sides:

ln(7^x) = ln10

x = ln10/ln7 = 1.18

17. 3^-x = 11

Take natural log on both sides :

ln(3^-x) = ln(11)

-x*ln3 = ln11

x = -ln11/ln3 = -2.18

19. (3/5)^x = 6^(2 -x)

take natural logon both sides:

x*ln(3/5) = (2 -x)ln6

x( ln (3/5) + ln6) =2ln6

x = 2ln6/( ln (3/5) + ln6)

= 3.583 /1.2809

x = 2.797

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.