Question 311578
I'll assume you meant log base 2:
{{{    log(2,x-1)+log(2,x+10)=3}}}
{{{    log(2,(x-1)(x+10))=3}}}
{{{    (x-1)(x+10)= 2^3}}}
{{{    x^2+10x-x-10 = 8 }}}
{{{    x^2+9x-10 = 8 }}}
{{{    x^2+9x-18 = 0 }}}
Solve by applying the quadratic formula.  Doing so yields:
x = {1.685, -10.685}
The negative solution is an extraneous solution leaving:
x = 1.685
Details of quadratic follows:
*[invoke quadratic "x", 1, 9, -18 ]