How do you solve $e^{ln x} = 12$ $e^lnx=12$ ?

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How do you solve $e^{ln x} = 12$ $e^lnx=12$ ?

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Answer 1 · 2016-05-08T23:52:09

$x = 12$ $x=12$

Explanation:

$ln (x)$ $color(red)(ln(x))$ means $the value k you need as an exponent of e for e^{k} to be equal to x$ $color(red)(" the value "k" you need as an exponent of e for " e^k" to be equal to x")$

Therefore
$XXX e^{ln (x)}$ $color(white)("XXX")color(blue)(e)^color(red)(ln(x))$
means
$XXX e$ $color(white)("XXX")color(blue)(e)$ raised to the exponent of $the value k you need as an exponent of e for e^{k} to be equal to x$ $color(red)(" the value "k" you need as an exponent of e for " e^k" to be equal to x")$

While this is a bit of a mind twister, if you think it though, what this means is that
$XXX e^{ln (x)} = x$ $color(white)("XXX")e^(ln(x))=x$

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How do you solve $e^{ln x} = 12$ $e^lnx=12$ ?

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