What is the value of x in the following expression?

$$x + \log_{10} (1 + 2^x) = x \log_{10} 5 + \log_{10} 6$$

The given equation can be written as 

$$\log\left(10\right)^{x\ }\ +\ \log\left(1+2^x\right)=\log\left(5\right)^x+\log6$$

$$\log\left(10\right)^{x\ }\left(1+2^x\right)=\log\left(5\right)^x\cdot6$$    (  since logA + logB=logAB)

$$\log\ \frac{\left(2^x\cdot5^x\right)\left(1+2^x\right)}{5^x\cdot6}=0$$    ( since logA - logB=logA/B)

$$\frac{\left(2^x\ +2^{2x\ }\right)}{6}=10^0$$  ($$Since\ \log_aN\ =x\ \ =>N=a^x$$)

$$2^{^x}+2^{2x}=6$$

The above  equation is satisfied only when x=1