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Answer :
The expression log((5x)/(7)) is equivalent to log5 + logx - log7, following the logarithmic properties of products and quotients. The correct option is 1.
The expression log((5x)/(7)) is equivalent to log5 + logx - log7. This is because of the properties of logarithms which state:
- The logarithm of a product of two numbers is the sum of the logarithms of those two numbers. Therefore, log(5x) can be written as log5 + logx.
- The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of those two numbers. Hence, log((5x)/7) translates to log5 + logx - log7.
Thus, the correct answer is option 1): log5 + logx - log7.
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