Nice Exponent/Logarithmic Math Simplification | Find the Value of X

Nice Exponent/Logarithmic Math Simplification | Find the Value of X

[@user-xv7xq3wt4x]

Would x=log base 6 of 36/43 be an acceptable answer to this problem

[@rickyahmadruslan1766]

Different question between your thumbnail and your expalanation

[@SuperAnangs]

I will try
Let 6^x=u
=> u/6+u+6u=6
=> u+6u+36u=36
=> 43u=36, u=36/43
---> please recall u=6^x
6^x=36/43
43×6^x=36
Approached by logarithm
-----> x log 6 + log 43= log 36
-----> x log 6 + log 43 = log 6^2
-----> x log 6 + log 43= 2 log 6
-----> x log 6= 2 log 6-log 43
Both sides divided by log 6
-----> x= 2 log 6/log 6-log 43/log 6
-----> x = 2-log 43/log 6