editing........

Deepak Aggarwal

Sania, sry but actually the question is not clear.

Is it 4log₉3 + 9 log₂4 = 10 log_x83 ? If yes, then your answer, i.e. x = (83)^1/2

NugoRama

4log(base 9)3 + 9log(base 2)4 = 10log(base x)83

4.1/2 + 9.2 = 10log(base x)83

20 = 10log(base x)83

log(base x)83 = 2

x^2 = 83

x = root(83) ..as deepak said.

Bipin Dubey

$10log_{x}83=4log_{9}3+9log_{2}4$

$10log_{x}83=4log_{9}9^{1/2}+9log_{2}2^{2}$

$10log_{x}83=4\left( \frac{1}{2}\right)+9(2)$

$10log_{x}83=20$

$log_{x}83=2$

$x^{2}=83$

$x=\sqrt[]{83}$