Final answer:
To solve log₂x = 3, we calculate 2 to the power of 3 which is 2x2x2, giving us the value of x as 8.
Step-by-step explanation:
If log₂x=3, then to find the value of x, we use the definition of a logarithm. This equation means 2 raised to what power equals x? Since the base of the logarithm is 2 and the logarithm itself is 3, we are looking for 2 raised to the power of 3, which is 2³.
Now substitute the known quantity into the equation and solve. Cubing of exponentials involves taking the cube (raising to the power of 3) of the digit term, so 2x2x2, which gives us 8. Thus, the value of x is 8. The property that log(aⁿ) = n × log(a) confirms that x is indeed 8.
To find x, we need to rewrite the logarithmic equation as an exponential equation. In this case, the base of the logarithm is 2, so we have 2 raised to the power of 3 equals x. Therefore, x = 23 = 8.