# How do you solve ln x + 2ln4 = ln7 - ln x?

Feb 2, 2016

$x = + \frac{\sqrt{7}}{4}$

#### Explanation:

From the given:

$\ln x + 2 \ln 4 = \ln 7 - \ln x$

$\ln x + \ln x = \ln 7 - 2 \ln 4$

$2 \ln x = \ln 7 - \ln \left({4}^{2}\right)$

$\ln {x}^{2} = \ln \left(\frac{7}{16}\right)$

${x}^{2} = \frac{7}{16}$

$x = \pm \frac{\sqrt{7}}{4}$ take the positive value as answer

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