What is x if $lnx + ln5x^2 = 10$ ?

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Answer 1 · 2015-11-10T08:52:41

First, you should use the logarithm rule
$log_a (x) + log_a (y) = log_a ( x * y)$

Here, it gives you:
$" ln x + ln 5 x^2 = 10$
$<=> " ln( x * 5 x^2) = 10$
$<=> " ln(5 x^3) = 10$

Now, you can exponentiate both sides to get rid of the $ln$ :

$<=> " e^(ln(5x^3)) = e^10$

... remember that $e$ and $ln$ are inverse functions...

$<=> " 5x^3 = e^10$
$<=> " x^3 = (e^10) / 5$
$<=> " x = root(3)((e^10) / 5)$

What is x if lnx + ln5x^2 = 10lnx + ln5x^2 = 10?