On the right side of the equation, x appears as part of a logarithm function,
and on the left side it appears not as part of a logarithm function.

There is no algebraic method for solving an equation which has its variable
appearing both as part of a logarithm function and also as not a part of a
logarithm function.  

All we can do is observe that if x=0, both sides are equal.

So x=0 is a solution.  Since the two functions defined by the two sides of the
equation, f(x)=0.06x and g(x)=ln(1+0.1x) are both strictly increasing functions,
they can only have x=0 as their common solution.  

Thus x=0 is the only solution.

Edwin

    


    Plot y = 0.06x (red) and y = ln(1+0.1x) (green).



It can not be solved using Algebra methods, but CAN BE solved NUMERICALLY.


Go to the site

    https://www.wolframalpha.com/widgets/view.jsp?id=a7d8ae4569120b5bec12e7b6e9648b86



Input the equation into the special window, click the "Submit" button and get the solution  x= 15.7901.