do you know this property for logarithms?

The property used is $\log_{b^\frac{m}{n}} a = \dfrac{n}{m} \log_{b} a$

Since $\sqrt{2187} = 3^{\frac{7}{2}}$ , we have $\log_{3^\frac 72} (x) = \frac{2}{7} \log_3 (x)$ $\implies a=2 ,b=7$ $\implies 10a+b=\boxed{27}$ .

Using logarithm property $\log_b a=\log_{b^n} a^n$ $\log_{\sqrt{2187}} (x) =\log_{3^\frac72} (x) = \log_{(3^\frac72)^\frac27} (x^\frac27) = \log_3 (x^\frac27) =\dfrac27 \log_3 (x)$ Therefore $a=2, b=7$ and $10a+b=\boxed{27}$