1. Solve for \( x \) in each equatio (a) \( \log 50+\log x=2 \)

1. We start with the equation: \[ \log 50 + \log x = 2 \] 2. Use the logarithm property: \[ \log a + \log b = \log (ab) \] so we can rewrite the equation as: \[ \log (50x) = 2 \] 3. Convert the logarithmic equation to its exponential form. Recall that: \[ \log_{10} y = k \quad \text{is equivalent to} \quad y = 10^k \] Therefore: \[ 50x = 10^2 \] 4. Calculate the right-hand side: \[ 10^2 = 100 \] which gives: \[ 50x = 100 \] 5. Solve for \( x \) by dividing both sides by 50: \[ x = \frac{100}{50} = 2 \] Thus, the solution is: \[ x = 2 \]