What is the solution of the equation

x log_{10} (10/3) + log_{10} 3 = log_{10} (2 + 3^{x}) + x?

- 10
- 3
- 1
- 0

**Answer**

x log_{10} (10/3) + log_{10} 3 = log_{10} (2 + 3^{x}) + x

x log_{10} 10 - x log_{10} 3 + log_{10} 3 = log_{10} (2 + 3^{x}) + x

x - x log_{10} 3 + log_{10} 3 = log_{10} (2 + 3^{x}) + x

log_{10} 3 - log_{10} 3^{x} = log_{10} (2 + 3^{x})

log_{10} (3/3^{x}) = log_{10} (2 + 3^{x})

3/3^{x} = 2 + 3^{x}

Let 3^{x} = t

3/t = 2 + t

t^{2} +2t - 3 = 0

t = -3, 1

3^{x} = 1

x = 0

**The correct option is D.**