Answer :
Using the properties of logarithms, the given equation simplifies to logx16 = logx4. From this, we can deduce that x is equal to 4.
Based on the question's equation: 4Logx + 5logx - 7logx = log164, we can utilize properties of logarithms to find x. Start by combining the logs on the left hand side using the property that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers (logb(XY) = logbX + logbY).
This reduces our equation to: 2logx = log164. We can then apply the rule that the logarithm of a number resulting from division of two numbers is the difference of the logarithms of the two numbers. This simplifies our equation to logx16 = logx4.
According to the rule that if two logs with the same base are equal, then the numbers they are logarithms of must also be equal, we can conclude that x = 16 / 4 = 4. Therefore, the correct value for x is 4.
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