Question 378051
Not sure if you meant {{{log(x,(x+3))=4}}} or {{{log((x(x+3)))=4}}}???
I'll work it both ways.
{{{log(x,(x+3))=4}}}
{{{x^4=x+3}}}
{{{x^4-x-3=0}}}
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{{{graph(300,300,-5,5,-5,5,0,x^4-x-3)}}}
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Using Newton's method to find the positive solution,
{{{f=x^4-x-3}}}
{{{df/dx=4x^3-1}}}
{{{x[1]=2}}}
{{{highlight(x=1.452627)}}}
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{{{log((x(x+3)))=4}}}
{{{x(x+3)=10^4}}}
{{{x^2+3x =10000}}}
{{{x^2+3x+9/4=10000+9/4}}}
{{{(x+3/2)^2=40009/4}}}
{{{x+3/2=0 +- sqrt(40009)/2}}}
{{{x=-3/2 +- sqrt(40009)/2}}}
{{{highlight(x=(-3 +- sqrt(40009))/2)}}}