Question #d7dac

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Question #d7dac

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Answer 1 · 2017-01-15T17:05:23

$x = e^{\frac{9}{2}}$ $x = e^(9/2)$

Explanation:

Using the property of logarithms that $ln (\frac{a}{b}) = ln a - ln b$ $ln(a/b) = lna - lnb$

and the property stating that ${ln a}^{b} = b ln a$ $lna^b = blna$

we can see that $ln x - 3 ln e = \frac{ln x}{3 ln e}$ $lnx - 3lne = lnx / (3lne)$

since $ln e = 1$ $lne = 1$ ,

$ln x - 3 = \frac{ln x}{3} \Rightarrow 3 ln x - 9 = ln x \Rightarrow 2 ln x = 9 \Rightarrow ln x = \frac{9}{2} \Rightarrow x = e^{\frac{9}{2}}$ $lnx - 3 = lnx / 3 => 3lnx - 9 = lnx => 2lnx = 9 => lnx = 9/2 => x = e^(9/2)$

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