Question 46193
s(x) = {{{log(7,x^2+7x+10)}}}
s(x) = {{{log(7,(x + 5)(x + 2))}}}
You can not take a logarithm of a negative number nor zero:
{{{x + 5 > 0}}}
{{{x > -5}}} check: {{{log(7,(x + 5)(x + 2))}}} = {{{log(7,(-4 + 5)(-4 + 2))}}} = {{{log(7,(1)(-2))}}} Nope
{{{x + 5 < 0}}}
{{{x < 5}}} check: {{{log(7,(x + 5)(x + 2))}}} = {{{log(7,(-6 + 5)(-6 + 2))}}} = {{{log(7,(-1)(-4))}}} = {{{log(7,(4))}}} Correct
and
{{{x + 2 > 0}}}
{{{x > -2}}} check: {{{log(7,(x + 5)(x + 2))}}} = {{{log(7,(1 + 5)(1 + 2))}}} = {{{log(7,(6)(3))}}} = {{{log(7,18)}}} Correct
Domain: x < -5 and -2 < x
{{{graph(600,600,-10,10,-10,10,log(7,x^2+7x+10))}}}