2022-11-11

Exponential and Logarithmic Functions
Find: ${\mathrm{log}}_{2}\left({x}^{2}-4x-28\right)=2$

Phiplyrhypelw0

Expert

Problem: We need to solve for x in the given equation
${\mathrm{log}}_{2}\left({x}^{2}-4x-28\right)=2$
Remember that if ${\mathrm{log}}_{a}\left(b\right)=y$, then ${a}^{y}=b$. In our equation, a=2, $b={x}^{2}-4x-28$, and y=2. Therefore ${x}^{2}-4x-28={2}^{2}=4$. This is easy to solve for.
${x}^{2}-4x-28=4$
${x}^{2}-4x-32=0$
Factor it
$\left(x-8\right)\left(x+4\right)=0$

Karley Castillo

Expert

${\mathrm{log}}_{2}\left({x}^{2}-4x-28\right)=2$
$\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}{x}^{2}-4x-28={2}^{2}=4$
${x}^{2}-4x-32=0$
$\left(x-8\right)\left(x+4\right)=0$

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