Final answer:
To solve the equation (X-1)log2=log31, divide both sides of the equation by log2 to isolate X. Use the change of base formula to rewrite the equation, then add 1 to both sides to solve for X. The rounded answer is X = 1.5680.
Step-by-step explanation:
To solve the equation (X-1)log2=log31, we can start by isolating the logarithmic term on one side of the equation. By dividing both sides of the equation by log2, we get X-1 = log31/log2. Next, we can use the change of base formula for logarithms to rewrite the equation as X-1 = log31/log2 = log31 / log2. Finally, we can add 1 to both sides of the equation to solve for X, giving us X = 1 + log31/log2. When we substitute the given values into the equation and round to four decimal places, we get X = 1.5680.