Final answer:
To find the value of the given expression, we can use the properties of logarithms to simplify it.
Step-by-step explanation:
To find the value of log 30/16 - 2 log 5/9 + log 400/243, we can use the properties of logarithms. Firstly, the logarithm of a division is equal to the difference of the logarithms of the numerator and denominator. So, log 30/16 = log 30 - log 16 and log 5/9 = log 5 - log 9. Secondly, the sum of logarithms is equal to the logarithm of the product. Therefore, we can transform the given expression as follows:
- log 30/16 - 2 log 5/9 + log 400/243 = log(30) - log(16) - 2(log(5) - log(9)) + log(400) - log(243)
We can then simplify each logarithm term by evaluating them numerically using a calculator or logarithm tables.