Final answer:
The real value of x is found by applying logarithmic properties to simplify the equation and then converting it to exponential form, yielding x = 125.
Step-by-step explanation:
To find the real value of x in the equation log₂ 24 - log₂ 3 = log₅ x, first apply the logarithmic property that the log of the division of two numbers is the difference of their logs. So we can rewrite the left-hand side of the equation as log₂(24/3). Simplify this to get log₂ 8, and since 8 is 2 to the third power, log₂ 8 is 3. Now, rewrite the equation as 3 = log₅ x.
To find x, recall the logarithm of a number is the exponent to which the base must be raised to get that number. This means we can rewrite the equation in exponential form as 5^3 = x. Calculating 5 to the third power gives us x = 125.