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How do you solve $ln 3 x = ln 15$ $ln 3x = ln 15$ ?

1 Answer

Oct 29, 2015

$x = 5$ $x=5$

Explanation:

In general if for some function
$XXX f (a) = (b)$ $color(white)("XXX")f(a) = (b)$
then one solution for $a$ $a$ is $a = b$ $a=b$
and if for this same function $f (c)$ $f(c)$ is unique for $\forall c$ $AAc$
then $a = b$ $a=b$ is a unique solution.

$ln (a)$ $ln(a)$ is a function of this form.

So
$XXX ln (3 x) = ln (15)$ $color(white)("XXX")ln(3x) = ln(15)$
implies
$XXX 3 x = 15$ $color(white)("XXX")3x=15$

Dividing both sides by 3 gives
$XXX x = 5$ $color(white)("XXX")x=5$

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