The value of $$(\log_{3}30)^{−1}+(\log_{4}900)^{−1}+(\log_{5}30)^{−1}$$ is

$$(\log_{3}30)^{−1}+(\log_{4}900)^{−1}+(\log_{5}30)^{−1}$$

$$\dfrac{1}{\log_330}+\dfrac{1}{\log_4900}+\dfrac{1}{\log_530}$$

$$\dfrac{1}{\log_330}+\dfrac{1}{\log_{2^2}{30^2}}+\dfrac{1}{\log_530}$$

$$\dfrac{1}{\log_330}+\dfrac{1}{\frac{2}{2}\log_230}+\dfrac{1}{\log_530}$$

$$\dfrac{1}{\log_330}+\dfrac{1}{\log_230}+\dfrac{1}{\log_530}$$

$$\log_{30}3+\log_{30}2+\log_{30}5$$

$$\log_{30}\left(3\times2\times5\right)$$

$$\log_{30}\left(30\right)=1$$