Final answer:
To solve the equation log₂ (9x + 2) = 2, convert it to exponential form, which gives 4 = 9x + 2. Solving for x, the answer is x = 2/9.
Step-by-step explanation:
The equation given is log₂ (9x + 2) = 2. To solve this equation, we first need to understand that the logarithm represents the exponent to which the base (in this case, 2) must be raised to obtain the value within the log function. Therefore, we can rewrite the equation in exponential form, where 2² equals 9x + 2. This effectively removes the logarithm and allows us to solve for x.
Moving forward with the calculation, we have:
- 2² = 4
- 4 = 9x + 2
- 4 - 2 = 9x
- 2 = 9x
- x = 2 / 9
The answer to the equation is x = 2/9.