Final answer:
The logarithmic equation log₂(x+15) = 6 is solved by converting it to its exponential form, 2^6 = x + 15, and then isolating x to find that x = 49.
Step-by-step explanation:
To solve the logarithmic equation log₂(x+15) = 6, we need to understand that a logarithmic equation relates the logarithm to the power the base must be raised to produce a certain number. In this case, the base is 2, and we are looking for the power to which 2 must be raised to equal x + 15. To solve, we can rewrite the logarithmic equation in its exponential form:
2^6 = x + 15
This means 2 raised to the power of 6 equals x + 15. Calculating 2^6 gives us 64, so:
64 = x + 15
To find the value of x, we subtract 15 from both sides of the equation:
x = 64 - 15
x = 49
Therefore, the solution to the equation log₂(x+15) = 6 is x = 49.