I interpret the first number in brackets as the base.You need a calculator to do this because, although the bases 2 and 4 are related to one another because 4 is 2 squared, there's no easy relation between 2 and 3, 3 and 10, or 2 and 10. 10 in base 2 is approximately 3.322; log 2 in base 10 is approximately 0.3010 which is the reciprocal of 3.322. Log 3 in base 2 is approximately 1.585 and log 2 in base 3 is 0.6309 which is the reciprocal of 1.585. Log 4 to base 2 is 2 so log 2 to base 4 is 0.5. To convert log x in one base to another we use the conversion factor of the log of one base of the other base. Let's choose base 2 as the common base. This is what the equation becomes: 0.5logx+logx+logx/log3=logx/log10. Put y=logx (base 2) and we get 0.5y+y+0.6903y=0.3010y. If we were to divide through by y we would have an inequality because 2.1903 is not equal to .3010. Therefore y=0 and logx=0, so x=1. That was the longwinded way of proving the solution.
We can see that x=1 makes all the terms in the original equation zero and 0=0 is always true!
Why go to all the trouble of using a calculator when the only answer is x=1? It was just possible that the sum of the numbers on the left side of the equation came to the result on the right side of the equation, in which case we would have had an identity instead of an equation, which would have been true for all values of x (except x=0).