How do I get exact results from Solve? [closed]

Question

When I evaluate

Solve[Log[-0.5 + 10^x + Sin[x]]/Log[10] == x, x]

I get the output

{{x -> ConditionalExpression[0.523599 + 6.28319 C[1], C[1] ∈ Integers]}, 
 {x -> ConditionalExpression[2.61799 + 6.28319 C[1], C[1] ∈ Integers]}}

How can I results in the form:

x -> π/6 + 2 π C[1]
x -> 5 π/6 + 2 π C[1]

Answer 1

@Szabolcs has already explained why you should replace .5 with 1/2. Perhaps you also want remove the ConditionalExpression wrapper. Then

Solve[Log[-1/2 + 10^x + Sin[x]]/Log[10] == x, x] /. 
  ConditionalExpression[arg_, ___] -> arg

{{x -> π/6 + 2 π C[1]}, {x -> (5 π)/6 + 2 π C[1]}}

is what you are looking for.