Solve for \( x \) in the equation \( \log_{10}(2\cos x) = 1 \).

Step 1 ：Step 1: Convert the logarithmic equation to an exponential equation: \( 10^1 = 2\cos x \).

Step 2 ：Step 2: Simplify the equation: \( \cos x = \frac{10}{2} \).

Step 3 ：Step 3: Solve for \( x \): \( x = \arccos(5) \). However, since the value of the cosine function lies in the interval [-1,1], there is no real solution to this equation as the value 5 is outside this range.