Final answer to the problem
$x=\frac{3+\sqrt{17}}{2},\:x=\frac{3-\sqrt{17}}{2}$
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Express the numbers in the equation as logarithms of base $2$
$\log_{2}\left(x-2\right)+\log_{2}\left(x+1\right)=\log_{2}\left(2^{2}\right)$
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$\log_{2}\left(x-2\right)+\log_{2}\left(x+1\right)=\log_{2}\left(2^{2}\right)$
Learn how to solve problems step by step online. log2(x+-2)+log2(x+1)=2. Express the numbers in the equation as logarithms of base 2. Apply the formula: \log_{a}\left(x\right)+\log_{a}\left(y\right)=\log_{a}\left(xy\right), where a=2, x=x-2 and y=x+1. Apply the formula: \log_{b}\left(b^a\right)=a, where a=2 and b=2. Apply the formula: x\left(a+b\right)=xa+xb, where a=x, b=1, x=x-2 and a+b=x+1.
Final answer to the problem
$x=\frac{3+\sqrt{17}}{2},\:x=\frac{3-\sqrt{17}}{2}$
