Final answer:
The solution to the logarithmic equation log₂(x+6)=3 is x = 2, determined by using the property that logarithms are inverses of exponentiation.
Step-by-step explanation:
The student has asked to solve the logarithmic equation log₂(x+6)=3. To solve this equation, we use the fact that logarithms are the inverses of exponentiation. So, this equation means that 2 raised to the power of 3 equals x + 6.
To find the value of x, we first calculate 2³, which is 8. Now, we have x + 6 = 8. Subtracting 6 from both sides gives us x = 2. Therefore, the solution to the equation log₂(x+6)=3 is x = 2.