[tex]\log_7(x^2+4x-11)=\dfrac52[/tex]
[tex]7^{\log_7(x^2+4x-11)}=7^{\frac52}[/tex]
[tex]x^2+4x-11=7^{\frac52}[/tex]
[tex]x^2+4x-\left(11+7^{\frac52}\right)=0[/tex]
Now you can use the quadratic formula to solve for [tex]x[/tex].
[tex]x=-2\pm\sqrt{15+7^{\frac52}}[/tex]
