Question 760180
logx to the base2=log2x+10 to the base root2
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{{{log(2,(x))=log(sqrt(2),(x+10))}}}
convert to base 2
{{{log(2,(x))=log(2,(x+10))/(1/2)log(2,(2))}}}
{{{log(2,(x))=log(2,(x+10))/(1/2)}}}
{{{log(2,(x))=2log(2,(x+10))}}}
{{{log(2,(x))=log(2,(x+10)^2)}}}
x=(x+10)^2=x^2+20x+100
x^2+19x+100=0
solve for x by quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
a=1, b=19, c=100
ans: no real roots, no solution.
see graph of quadratic equation below:
{{{ graph( 300, 300, -20, 10, -10, 40,x^2+19x+100) }}}