Exercise ID325

Algebra → Logarithm → Logarithm equations
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Evaluate the following expression:

${\mathrm{log}}_{\sqrt{2}}\left(x\right)+{\mathrm{log}}_{2}\left(x\right)+{\mathrm{log}}_{\sqrt{8}}\left(x\right)=11\phantom{\rule{0ex}{0ex}}$

${\mathrm{log}}_{{2}^{\frac{1}{2}}}x+{\mathrm{log}}_{2222}x+{\mathrm{log}}_{{2}^{\frac{3}{2}}}x=11\phantom{\rule{0ex}{0ex}}$ $2{\mathrm{log}}_{2}\left(x\right)+{\mathrm{log}}_{2}\left(x\right)+\frac{2}{3}{\mathrm{log}}_{2}\left(x\right)=11\phantom{\rule{0ex}{0ex}}$ $3\frac{2}{3}{\mathrm{log}}_{2}\left(x\right)=11\phantom{\rule{0ex}{0ex}}$ $\frac{11}{3}{\mathrm{log}}_{2}\left(x\right)=11\phantom{\rule{0ex}{0ex}}$ ${\mathrm{log}}_{2}\left(x\right)=\frac{\frac{11}{1}}{\frac{11}{3}}\phantom{\rule{0ex}{0ex}}$ ${\mathrm{log}}_{2}\left(x\right)=3\phantom{\rule{0ex}{0ex}}$ $x={2}^{3}\phantom{\rule{0ex}{0ex}}$ $x=8\phantom{\rule{0ex}{0ex}}$
$x=8\phantom{\rule{0ex}{0ex}}$