Final answer:
By leveraging the properties of logarithms, the equation log₉₄ + log₉₅ = log₉x + log₉₁₀ can be simplified to show that x = 2.
Step-by-step explanation:
The equation provided is log₉₄ + log₉₅ = log₉x + log₉₁₀. To solve for x, we can take advantage of the property of logarithms that states: the logarithm of a product of two numbers is the sum of the logarithms of those two numbers. Hence, we can rewrite the equation as log₉(4•5) = log₉(x•10). Then, we can deduce that 4•5 must equal x•10 to satisfy the equality (since log₉ is a one-to-one function, meaning if log₉a = log₉b, then a = b).
Therefore, solving for x involves the following step: x•10 = 4•5, and thus x = (4•5)/10. Simplifying, we get x = 2. So the solution to the equation is x = 2.