# Exercise ID332

Algebra → Logarithm → Logarithm equations
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Evaluate the following expression:

${\mathrm{log}}_{4}\left(x+2\right)×{\mathrm{log}}_{x}\left(2\right)=1\phantom{\rule{0ex}{0ex}}$

${\mathrm{log}}_{{2}^{2}}\left(x+2\right)×\frac{1}{{\mathrm{log}}_{2}\left(x\right)}=1\phantom{\rule{0ex}{0ex}}$ $\frac{1}{2}{\mathrm{log}}_{2}\left(x+2\right)×\frac{1}{{\mathrm{log}}_{2}\left(x\right)}=1\phantom{\rule{0ex}{0ex}}$ ${\mathrm{log}}_{2}{\left(x+2\right)}^{\frac{1}{2}}={\mathrm{log}}_{2}\left(x\right)\phantom{\rule{0ex}{0ex}}$ $x+2={x}^{2}\phantom{\rule{0ex}{0ex}}$ $-{x}^{2}+x+2=0\phantom{\rule{0ex}{0ex}}$ ${x}_{1,2}=\frac{-1±\sqrt{1+8}}{-2}\phantom{\rule{0ex}{0ex}}$ ${x}_{1,2}=\frac{-1±3}{-2}\phantom{\rule{0ex}{0ex}}$