I attach a graph I produced in Excel, to show the result when and . For these values, the equation has the approximate solution , which I found this value using Excel's 'Goal Seek'. There is also another branch of the log graph for values of less than , which I haven't included in the diagram.
You'll see that there are no points on the log graph where , and as , the graph from below. So there won't be any solution if for positive values of .
I'll leave you to work out what will happen to the graphs for different values of and .