Question

Solve the equation to find the value

log 2 (5x – 4) = 4
Student's Answer
Student's Work
A. 6/5
B. 4
C. 8
D. 256/5

Answer 1

The answer is A, 6/5. I show my solving steps in the attached image

Answer 2

To solve the equation log2(5x – 4) = 4, start by isolating the logarithmic expression and then apply the inverse function of logarithm. Finally, divide both sides by 5 to find the value of x, which is 4.

Step-by-step explanation:

To solve the equation log2(5x – 4) = 4, we need to isolate the logarithmic expression and solve for x. Here are the steps:

1. Start by applying the inverse function of logarithm, which is the exponentiation function. Raise both sides of the equation to the base 2: 2log2(5x – 4) = 24.
2. By definition, the exponentiation function and the logarithmic function cancel each other out. This leaves us with 5x – 4 = 16.
3. Add 4 to both sides of the equation to isolate x: 5x = 20.
4. Finally, divide both sides by 5 to find the value of x: x = 4.

Therefore, the solution to the equation is x = 4.