Use logarithms to solve the equation $7^{x}=2^{x+1}$, giving the value of x correct to 3 significant figures.

$7^{x}=2^{x+1}$
$\log 7^{x}=\log 2^{x+1} \\ \\ \therefore x\log 7=\left( x+1\right) \log 2 \\ \\ x\log 7=x\log 2+\log 2 \\ \\ x\log 7-x\log 2=\log 2 \\ \\ x\left( \log 7-\log 2\right) =\log 2 \\ \\ x=\dfrac {\log 2}{\log 7-\log 2} \\ \\ x=0.553$