Log2 (3x-1) = log2 (x+8)

If you need answers for the whole assignment

Step-by-step explanation:

1. Consider 8^x-4 = 8^10

Because the (blank a) are equal, the (blank b) must also be equal.

Answer: Bases, Exponents

The solution to the equation is 14

2. What equation is equivalent to 9^ (x-3) = 729?

Answer 3^x - 3 = 3^6

Solve: 9x - 3 = 729

Answer: x = 6

3. To solve 5 (2^x+4) = 15, first divide each side by

Answer: 5

Solve 5 (2^x+4) = 15. Round to the nearest thousandth.

Answer: - 2.415

4. Which of the following is the solution of 5e^2x - 4 = 11?

Answer: x=In3/2

5. Select all of the potential solution (s) of the equation 2log5x = log54.

Answer: 2,-2

What is the solution to 2log5x = log54?

Answer: 2

6. Which equation is equivalent to log5x3 - logx2 = 2?

Answer: 10^log5^3/x^2=10^2

Solve: log5x3 - logx2 = 2

Answer: 20

7. What is the solution to ln (x2 - 16) = 0?

Answer: x= + - (17)

8. Solve: ln 2x + ln 2 = 0

Answer: ¼

Solve: e^ 2x+5 = 4

Answer: x = (In4) - 5/2

9. Consider the equation log (3x - 1) = log2 (8). Explain why 3x - 1 is not equal to Describe the steps you would take to solve the equation, and state what 3x - 1 is equal to.

Answer: The bases are not the same, so you cannot set 3x - 1 equal to 8. You can evaluate the logarithm on the right side of the equation to get. You can use the definition of a logarithm to write 3x - 1 = 1000.

10. An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation 100e^0.05t = 150 represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use your calculator and round to the nearest whole number.

Answer: 8

X = 9/2

Alternative form

x=4 1/2, x=4.5

Step-by-step explanation:

* = Multiply

1. log (little 10 under) (2) * (3x-1) = log (little 10 under) (2) * (x+8)

2. then divide both side by log (little 10 under (2))

3. 3x-1=x+8

4. move variable to the left side and change its sign

5. 3x-x-1=8

6. then move constant to the right side and change its sign

7. 3x-x=8+1

8. collect like terms

9. 2x=8+1

10. add 8+1

11. 2x=9

12. then divide both sides by 2

13. 2/2 9/2

14. 2/2 cancels out so x=9/2 is the answer