How do you solve ${ln x}^{3} = 2 ln 5 - 3 ln 2$ $ln x^3 = 2 ln 5 - 3 ln 2$ ?

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How do you solve ${ln x}^{3} = 2 ln 5 - 3 ln 2$ $ln x^3 = 2 ln 5 - 3 ln 2$ ?

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Answer 1 · 2016-04-21T19:45:35

$x = \sqrt[3]{\frac{25}{8}} = \frac{\sqrt[3]{25}}{2}$ $x=root3(25/8)=root3 25 / 2$

Explanation:

${ln x}^{3} - 2 ln 5 + 3 ln 2 = 0$ $lnx^3-2ln5+3ln2=0$
${ln x}^{3} - {ln 5}^{2} + {ln 2}^{3} = 0$ $lnx^3-ln5^2+ln2^3=0$
${ln x}^{3} - ln 25 + ln 8 = 0$ $lnx^3-ln25+ln8=0$
$ln (\frac{8 x^{3}}{25}) = 0$ $ln((8x^3)/25)=0$
$e^{0} = \frac{8 x^{3}}{25}$ $e^0=(8x^3)/25$

$1 = \frac{8 x^{3}}{25}$ $1=(8x^3)/25$

$25 = 8 x^{3}$ $25=8x^3$

$\frac{25}{8} = x^{3}$ $25/8=x^3$

$x = \sqrt[3]{\frac{25}{8}} = \frac{\sqrt[3]{25}}{2}$ $x=root3(25/8)=root3 25 / 2$

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How do you solve ${ln x}^{3} = 2 ln 5 - 3 ln 2$ $ln x^3 = 2 ln 5 - 3 ln 2$ ?

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Explanation:

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