As far as I know it's not possible. If you need the log10 trendline equation, your best bet would probably be to calculate the log10 of the x axis in a helper column, then use the slope and intercept worksheet functions to calculate the coefficients. The form of the equation would be Y = slope * log10x + intercept.
Isn't the trendline the same? I think it's only the coefficient of the logarithm in the equation that changes.
As you know if you divide the logarithms of any number in 2 different bases you get a constant. You can therefore replace the logarithm in a base by the logarithm in another base just by multiplying by that constant.
Ex. You display the trendline equation in the chart: