Super Logarithm!

Firstly we have to find the prime factors of $759375$ .

$759375= (3\times5)^{5} =3^{5} \times 5^{5}$

This question can be written in the other way to make it easier to solve.

$log_{3x}759375=x$ can be written as: $3x^{x}=759375$

$(3 \times x)^{x}=3^{5} \times 5^{5}$

$3^{x} \times x^{x}=3^{5} \times 5^{5}$

So, $x=5$

Thus, the answer is: $x=\boxed{5}$

First, factor the given number

(%i3) factor(759375);
                                      5  5
(%o3)                                3  5

$log_{3x}759375 = x\\ \implies 759375 = (3x)^x\\ \implies 3^55^5 =3^x x^x\\ \implies x = 5$