Final answer:
The equation is solved using logarithm properties to simplify and equate the arguments, leading to x = 6.43 after solving the resulting algebraic equation.
Step-by-step explanation:
The question involves solving an equation with logarithms, utilizing the properties of logarithms. We are given the equation 1 × log(2x - 9) = log(3x) - log(5). We can use the property that the logarithm of a quotient is the difference between the logarithms of the numerator and the denominator, which allows us to rewrite the equation as log(2x - 9) = log(3x/5).
To solve the equation, we equate the arguments of the logarithms because if log(a) = log(b), then a = b. This gives us 2x - 9 = 3x/5. Multiplying both sides by 5 to eliminate the fraction, we get 10x - 45 = 3x. Solving for x, we subtract 3x from both sides to get 7x - 45 = 0, and then add 45 to both sides which yields 7x = 45. Finally, dividing by 7 gives us x = 45/7, which simplifies to approximately x = 6.43 (rounded to two decimal places).