Answer :
The given expression log₅ 6 + log₃ 7 = log₅ 42 is incorrect because it combines logarithms with different bases, which is not allowed by the properties of logarithms.
To solve this problem, we need to understand the properties of logarithms. According to the properties of logarithms, specifically the property that deals with the sum of logarithms, we have:
- logₐ x + logₐ y = logₐ (xy)
This property only applies when the logarithms have the same base. In this problem, the bases of the logarithms are different: one is base 5 and the other is base 3. Thus, the property cannot be applied directly.
The error can be identified as follows:
- Error Identification: The given expression log₅ 6 + log₃ 7 = log₅ 42 incorrectly applies the property of the sum of logarithms on logarithms with different bases.
- Explanation: The sum of logarithms log₅ 6 and log₃ 7 cannot be combined directly because their bases are different. The property logₐ x + logₐ y = logₐ (xy) requires that both logarithms have the same base 'a'.