Expressing $\log_{0.985} (0.1)$ only using $\ln$ and $\log_{10}$

Question

How to express $\log_{0.985}(0.1)$ only using $\ln$ and $\log_{10}$ functions, if it is possible?

Thanks in advance!

Answer 1

$$\log_{a}(b)=\frac{\ln(b)}{\ln(a)}=\frac{\log_{10}(b)}{\log_{10}(a)}$$

Answer 2

By change of base rule of logarithms we have:

$$\log_{0.985}0.1=\dfrac{\log_{10}0.1}{\log_{10}0.985}=\dfrac{-1}{\log_{10}0.985}=\dfrac{-\ln0.985}{\ln 10}$$