ĐKXĐ: \(x>-1\)
\(log_4\left(x+7\right)>log_2\left(x+1\right)\)
\(\Leftrightarrow\dfrac{1}{2}log_2\left(x+7\right)>log_2\left(x+1\right)\)
\(\Leftrightarrow log_2\left(x+7\right)>2log_2\left(x+1\right)=log_2\left(x+1\right)^2\)
\(\Rightarrow x+7>\left(x+1\right)^2\)
\(\Rightarrow x^2+x-6< 0\)
\(\Rightarrow-3< x< 2\)
Kết hợp ĐKXĐ \(\Rightarrow-1< x< 2\Rightarrow x=\left\{0;1\right\}\) có 2 nghiệm nguyên