How do you solve $ln 2 + ln x = 5$ ?

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Answer 1 · 2015-11-14T03:25:53

$x = e^5/2$

We will use the following properties of logarithms:
$ln(x) + ln(y) = ln(xy)$
$e^(ln(x)) = x$

$ln(2) + ln(x) = 5$

$=> ln(2x) = 5$ (by the first property)

$=> e^(ln(2x)) = e^5$

$=>2x = e^5$ (by the second property)

$=> x = e^5/2$

How do you solve ln 2 + ln x = 5ln 2 + ln x = 5?