Final answer:
The solution to the equation log₁₀x - log₁₀(28) = log₁₀(27) is obtained by applying the property of logarithms. Simplifying the equation by combining the logarithms shows that x must equal 27 multiplied by 28, which gives x = 756.
Step-by-step explanation:
The student's question involves solving the equation log₁₀x - log₁₀(28) = log₁₀(27) using logarithmic properties. To solve this equation, we will apply the property of logarithms which states that the logarithm of a number resulting from the division of two numbers is the difference between the logarithms of these two numbers. Therefore, we can rewrite the equation as log₁₀(x/28) = log₁₀(27).
Next, we understand that if log₁₀(A) = log₁₀(B), then A must equal B. Applying this principle to our equation gives us x/28 = 27. Multiplying both sides by 28 yields x = 27 × 28. Simplifying that, we find x = 756. Hence, the value of x that satisfies the original equation is 756.