[tex]\left(\dfrac{1}{7}\right)^x+\left(\dfrac{1}{7}\right)^{x+1}=56\\\\\left(\dfrac{1}{7}\right)^x+\left(\dfrac{1}{7}\right)^x\cdot\dfrac{1}{7}=56\\\\\left(\dfrac{1}{7}\right)^x\left(1+\dfrac{1}{7}\right)=56\\\\\left(\dfrac{1}{7}\right)^x\cdot\dfrac{8}{7}=56\\\\\left(\dfrac{1}{7}\right)^x=49\\\\7^{-x}=7^2\\-x=2\\x=-2[/tex]
