Solve the logarithmic equation. \[ 1+\log (3 x-10)=0 \] Write an equation in exponential form after the definition of logarithms is used. (Use integers or fractions for any numbers in the equation.)

Step 1 ：Given the logarithmic equation \(1+\log (3 x-10)=0\)

Step 2 ：Subtract 1 from both sides of the equation to isolate the logarithm, resulting in \(\log (3 x-10) = -1\)

Step 3 ：Convert the logarithmic equation to an exponential equation using the definition of logarithms. The definition of logarithms states that if \(\log_b(a) = c\), then \(b^c = a\). In this case, b is 10 (since the base of the logarithm is not specified, it is assumed to be 10), a is 3x - 10, and c is -1. This gives us \(10^{-1} = 3x - 10\)

Step 4 ：Solve the equation for x, resulting in \(x = \frac{101}{30}\)

Step 5 ：Final Answer: The exponential form of the equation is \(10^{-1} = 3x - 10\) and the solution to the equation is \(\boxed{x = \frac{101}{30}}\)