What is x if Ln9+ln4x^2=2?

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What is x if Ln9+ln4x^2=2?

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Answer 1 · 2018-05-04T00:11:24

We wish to find $x$ $x$ if $ln 9 + ln (4 x^{2}) = 2$ $ln9 + ln(4x^2) = 2$ . We will need to use some log rules here. Specifically, recall that:

$ln x + ln y = ln (x y)$ $lnx + lny = ln(xy)$
$e^{ln (x)} = x$ $e^(ln(x)) = x$

Using the above two rules, we can quickly come to an answer.

$ln 9 + ln (4 x^{2}) = 2$ $ln 9 + ln(4x^2) = 2$ (Use Rule 1 to combine.)
$ln (9 \cdot 4 x^{2}) = 2$ $ln(9*4x^2) = 2$
$ln (36 x^{2}) = 2$ $ln(36x^2) = 2$ (Use Rule 2 and exponentiate both sides.)
$36 x^{2} = e^{2}$ $36x^2 = e^2$
$x^{2} = \frac{e^{2}}{36} = {(\frac{e}{6})}^{2}$ $x^2 = e^2/(36) = (e/6)^2$
$x = \pm \frac{e}{6}$ $x = pm e/6$

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What is x if Ln9+ln4x^2=2?

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